The peculiar notion of exchange forces - II: From nuclear forces to QED, 1929-1950

Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics

Volumn 27, Issue 2, 1996, Pages 99-131

  Carson, Cathryn ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030162097     PISSN: 13552198     EISSN: 18792502     Source Type: Journal    
DOI: 10.1016/1355-2198(95)00003-8     Document Type: Article

References (181)

1. 1 W. Heisenberg, 'Über den Bau der Atomkerne, I, II, III', Zeitschrift für Physik 77 (1932), 1-11; Zeitschrift für Physik 78 (1932), 156-164; Zeitschrift für Physik 80 (1933), 587-596. Secondary literature includes Joan Bromberg, 'The Impact of the Neutron: Bohr and Heisenberg', Historical Studies in the Physical and Biological Sciences 3 (1971), 307-341; Arthur I. Miller, 'Redefining Visualizability', in Imagery in Scientific Thought: Creating 20th-century Physics (Boston: Birkhäuser, 1984), pp. 125-183; Arthur I. Miller, 'Werner Heisenberg and the Beginning of Nuclear Physics', Physics Today 38(11) (1985), 60-68; Laurie M. Brown and Helmut Rechenberg, 'Nuclear Structure and Beta Decay (1932-1933)', American Journal of Physics 56 (1988), 982-988; Arthur I. Miller, 'Theories of the Nuclear Force in the 1930s', in Early Quantum Electrodynamics: A Source Book (Cambridge: Cambridge University Press, 1994), pp. 84-95.
2. 1 W. Heisenberg, 'Über den Bau der Atomkerne, I, II, III', Zeitschrift für Physik 77 (1932), 1-11; Zeitschrift für Physik 78 (1932), 156-164; Zeitschrift für Physik 80 (1933), 587-596. Secondary literature includes Joan Bromberg, 'The Impact of the Neutron: Bohr and Heisenberg', Historical Studies in the Physical and Biological Sciences 3 (1971), 307-341; Arthur I. Miller, 'Redefining Visualizability', in Imagery in Scientific Thought: Creating 20th-century Physics (Boston: Birkhäuser, 1984), pp. 125-183; Arthur I. Miller, 'Werner Heisenberg and the Beginning of Nuclear Physics', Physics Today 38(11) (1985), 60-68; Laurie M. Brown and Helmut Rechenberg, 'Nuclear Structure and Beta Decay (1932-1933)', American Journal of Physics 56 (1988), 982-988; Arthur I. Miller, 'Theories of the Nuclear Force in the 1930s', in Early Quantum Electrodynamics: A Source Book (Cambridge: Cambridge University Press, 1994), pp. 84-95.
3. 1 W. Heisenberg, 'Über den Bau der Atomkerne, I, II, III', Zeitschrift für Physik 77 (1932), 1-11; Zeitschrift für Physik 78 (1932), 156-164; Zeitschrift für Physik 80 (1933), 587-596. Secondary literature includes Joan Bromberg, 'The Impact of the Neutron: Bohr and Heisenberg', Historical Studies in the Physical and Biological Sciences 3 (1971), 307-341; Arthur I. Miller, 'Redefining Visualizability', in Imagery in Scientific Thought: Creating 20th-century Physics (Boston: Birkhäuser, 1984), pp. 125-183; Arthur I. Miller, 'Werner Heisenberg and the Beginning of Nuclear Physics', Physics Today 38(11) (1985), 60-68; Laurie M. Brown and Helmut Rechenberg, 'Nuclear Structure and Beta Decay (1932-1933)', American Journal of Physics 56 (1988), 982-988; Arthur I. Miller, 'Theories of the Nuclear Force in the 1930s', in Early Quantum Electrodynamics: A Source Book (Cambridge: Cambridge University Press, 1994), pp. 84-95.
4. 1 W. Heisenberg, 'Über den Bau der Atomkerne, I, II, III', Zeitschrift für Physik 77 (1932), 1-11; Zeitschrift für Physik 78 (1932), 156-164; Zeitschrift für Physik 80 (1933), 587-596. Secondary literature includes Joan Bromberg, 'The Impact of the Neutron: Bohr and Heisenberg', Historical Studies in the Physical and Biological Sciences 3 (1971), 307-341; Arthur I. Miller, 'Redefining Visualizability', in Imagery in Scientific Thought: Creating 20th-century Physics (Boston: Birkhäuser, 1984), pp. 125-183; Arthur I. Miller, 'Werner Heisenberg and the Beginning of Nuclear Physics', Physics Today 38(11) (1985), 60-68; Laurie M. Brown and Helmut Rechenberg, 'Nuclear Structure and Beta Decay (1932-1933)', American Journal of Physics 56 (1988), 982-988; Arthur I. Miller, 'Theories of the Nuclear Force in the 1930s', in Early Quantum Electrodynamics: A Source Book (Cambridge: Cambridge University Press, 1994), pp. 84-95.
5. 1 W. Heisenberg, 'Über den Bau der Atomkerne, I, II, III', Zeitschrift für Physik 77 (1932), 1-11; Zeitschrift für Physik 78 (1932), 156-164; Zeitschrift für Physik 80 (1933), 587-596. Secondary literature includes Joan Bromberg, 'The Impact of the Neutron: Bohr and Heisenberg', Historical Studies in the Physical and Biological Sciences 3 (1971), 307-341; Arthur I. Miller, 'Redefining Visualizability', in Imagery in Scientific Thought: Creating 20th-century Physics (Boston: Birkhäuser, 1984), pp. 125-183; Arthur I. Miller, 'Werner Heisenberg and the Beginning of Nuclear Physics', Physics Today 38(11) (1985), 60-68; Laurie M. Brown and Helmut Rechenberg, 'Nuclear Structure and Beta Decay (1932-1933)', American Journal of Physics 56 (1988), 982-988; Arthur I. Miller, 'Theories of the Nuclear Force in the 1930s', in Early Quantum Electrodynamics: A Source Book (Cambridge: Cambridge University Press, 1994), pp. 84-95.
6. 1 W. Heisenberg, 'Über den Bau der Atomkerne, I, II, III', Zeitschrift für Physik 77 (1932), 1-11; Zeitschrift für Physik 78 (1932), 156-164; Zeitschrift für Physik 80 (1933), 587-596. Secondary literature includes Joan Bromberg, 'The Impact of the Neutron: Bohr and Heisenberg', Historical Studies in the Physical and Biological Sciences 3 (1971), 307-341; Arthur I. Miller, 'Redefining Visualizability', in Imagery in Scientific Thought: Creating 20th-century Physics (Boston: Birkhäuser, 1984), pp. 125-183; Arthur I. Miller, 'Werner Heisenberg and the Beginning of Nuclear Physics', Physics Today 38(11) (1985), 60-68; Laurie M. Brown and Helmut Rechenberg, 'Nuclear Structure and Beta Decay (1932-1933)', American Journal of Physics 56 (1988), 982-988; Arthur I. Miller, 'Theories of the Nuclear Force in the 1930s', in Early Quantum Electrodynamics: A Source Book (Cambridge: Cambridge University Press, 1994), pp. 84-95.
7. 1 W. Heisenberg, 'Über den Bau der Atomkerne, I, II, III', Zeitschrift für Physik 77 (1932), 1-11; Zeitschrift für Physik 78 (1932), 156-164; Zeitschrift für Physik 80 (1933), 587-596. Secondary literature includes Joan Bromberg, 'The Impact of the Neutron: Bohr and Heisenberg', Historical Studies in the Physical and Biological Sciences 3 (1971), 307-341; Arthur I. Miller, 'Redefining Visualizability', in Imagery in Scientific Thought: Creating 20th-century Physics (Boston: Birkhäuser, 1984), pp. 125-183; Arthur I. Miller, 'Werner Heisenberg and the Beginning of Nuclear Physics', Physics Today 38(11) (1985), 60-68; Laurie M. Brown and Helmut Rechenberg, 'Nuclear Structure and Beta Decay (1932-1933)', American Journal of Physics 56 (1988), 982-988; Arthur I. Miller, 'Theories of the Nuclear Force in the 1930s', in Early Quantum Electrodynamics: A Source Book (Cambridge: Cambridge University Press, 1994), pp. 84-95.
8. 1 W. Heisenberg, 'Über den Bau der Atomkerne, I, II, III', Zeitschrift für Physik 77 (1932), 1-11; Zeitschrift für Physik 78 (1932), 156-164; Zeitschrift für Physik 80 (1933), 587-596. Secondary literature includes Joan Bromberg, 'The Impact of the Neutron: Bohr and Heisenberg', Historical Studies in the Physical and Biological Sciences 3 (1971), 307-341; Arthur I. Miller, 'Redefining Visualizability', in Imagery in Scientific Thought: Creating 20th-century Physics (Boston: Birkhäuser, 1984), pp. 125-183; Arthur I. Miller, 'Werner Heisenberg and the Beginning of Nuclear Physics', Physics Today 38(11) (1985), 60-68; Laurie M. Brown and Helmut Rechenberg, 'Nuclear Structure and Beta Decay (1932-1933)', American Journal of Physics 56 (1988), 982-988; Arthur I. Miller, 'Theories of the Nuclear Force in the 1930s', in Early Quantum Electrodynamics: A Source Book (Cambridge: Cambridge University Press, 1994), pp. 84-95.
9. 2 Heisenberg, op. cit., note 1, I, p. 1.
10. 3 Roger Stuewer, 'The Nuclear Electron Hypothesis', in William R. Shea (ed.), Otto Hahn and the Rise of Nuclear Physics (Dordrecht: Reidel, 1983), pp. 29-42; E. Teller, 'Stand und Grenzen der heutigen Theorien über den Kernaufbau', in A. Eucken, O. Lummer and E. Waetzmann (eds), Müller-Pouillets Lehrbuch der Physik, 11th edn, Vol. 4, Part 3 (Braunschweig: Friedrich Vieweg, 1933), pp. 546-554; cf. Niels Bohr, 'Atomic Stability and Conservation Laws', in Convegno di Fisica Nucleare, Ottobre 1931 (Rome: Reale Accademia d'Italia, 1932), pp. 119-130, reprinted in Niels Bohr, Collected Works, Rudolf Peierls (ed.), Vol. 9, Nuclear Physics (1929-1952) (Amsterdam: North-Holland, 1986), pp. 103-114.
11. 3 Roger Stuewer, 'The Nuclear Electron Hypothesis', in William R. Shea (ed.), Otto Hahn and the Rise of Nuclear Physics (Dordrecht: Reidel, 1983), pp. 29-42; E. Teller, 'Stand und Grenzen der heutigen Theorien über den Kernaufbau', in A. Eucken, O. Lummer and E. Waetzmann (eds), Müller-Pouillets Lehrbuch der Physik, 11th edn, Vol. 4, Part 3 (Braunschweig: Friedrich Vieweg, 1933), pp. 546-554; cf. Niels Bohr, 'Atomic Stability and Conservation Laws', in Convegno di Fisica Nucleare, Ottobre 1931 (Rome: Reale Accademia d'Italia, 1932), pp. 119-130, reprinted in Niels Bohr, Collected Works, Rudolf Peierls (ed.), Vol. 9, Nuclear Physics (1929-1952) (Amsterdam: North-Holland, 1986), pp. 103-114.
12. 3 Roger Stuewer, 'The Nuclear Electron Hypothesis', in William R. Shea (ed.), Otto Hahn and the Rise of Nuclear Physics (Dordrecht: Reidel, 1983), pp. 29-42; E. Teller, 'Stand und Grenzen der heutigen Theorien über den Kernaufbau', in A. Eucken, O. Lummer and E. Waetzmann (eds), Müller-Pouillets Lehrbuch der Physik, 11th edn, Vol. 4, Part 3 (Braunschweig: Friedrich Vieweg, 1933), pp. 546-554; cf. Niels Bohr, 'Atomic Stability and Conservation Laws', in Convegno di Fisica Nucleare, Ottobre 1931 (Rome: Reale Accademia d'Italia, 1932), pp. 119-130, reprinted in Niels Bohr, Collected Works, Rudolf Peierls (ed.), Vol. 9, Nuclear Physics (1929-1952) (Amsterdam: North-Holland, 1986), pp. 103-114.
13. 3 Roger Stuewer, 'The Nuclear Electron Hypothesis', in William R. Shea (ed.), Otto Hahn and the Rise of Nuclear Physics (Dordrecht: Reidel, 1983), pp. 29-42; E. Teller, 'Stand und Grenzen der heutigen Theorien über den Kernaufbau', in A. Eucken, O. Lummer and E. Waetzmann (eds), Müller-Pouillets Lehrbuch der Physik, 11th edn, Vol. 4, Part 3 (Braunschweig: Friedrich Vieweg, 1933), pp. 546-554; cf. Niels Bohr, 'Atomic Stability and Conservation Laws', in Convegno di Fisica Nucleare, Ottobre 1931 (Rome: Reale Accademia d'Italia, 1932), pp. 119-130, reprinted in Niels Bohr, Collected Works, Rudolf Peierls (ed.), Vol. 9, Nuclear Physics (1929-1952) (Amsterdam: North-Holland, 1986), pp. 103-114.
14. 4 The German text contains the phrase 'auf das Neutron abzuschieben'; this can be rendered more graphically as 'to shove into the neutron', which also describes Heisenberg's approach. Heisenberg to Bohr, 20 June 1932, Archive for History of Quantum Physics.
15. 5 It has been suggested that Heisenberg did need loose electrons in the nucleus to explain β-decay and the Meitner-Hupfeld effect (see below). This interpretation seems to stem, however, from passages in the third paper in which Heisenberg describes the consequences of making another assumption about the neutron, namely, that it is an elementary particle with no electron inside. Ibid., pp. 594-595; cf. Laurie M. Brown and Donald F. Moyer, 'Lady or Tiger? - The Meitner-Hupfeld Effect and Heisenberg's Neutron Theory', American Journal of Physics 52 (1984), 130-136.
16. 5 It has been suggested that Heisenberg did need loose electrons in the nucleus to explain β-decay and the Meitner-Hupfeld effect (see below). This interpretation seems to stem, however, from passages in the third paper in which Heisenberg describes the consequences of making another assumption about the neutron, namely, that it is an elementary particle with no electron inside. Ibid., pp. 594-595; cf. Laurie M. Brown and Donald F. Moyer, 'Lady or Tiger? - The Meitner-Hupfeld Effect and Heisenberg's Neutron Theory', American Journal of Physics 52 (1984), 130-136.
17. 6 Brown and Moyer, op. cit., note 5.
18. 7 Heisenberg, op. cit., note 1, I, p. 1.
19. 8 E.g. Heisenberg, op. cit., note 1, I, pp. 1, 2; II, pp. 160, 163, 164; III, p. 594. The distinction between constituents and particles is made in Brown and Rechenberg, op. cit., note 1.
20. 8 E.g. Heisenberg, op. cit., note 1, I, pp. 1, 2; II, pp. 160, 163, 164; III, p. 594. The distinction between constituents and particles is made in Brown and Rechenberg, op. cit., note 1.
21. 8 E.g. Heisenberg, op. cit., note 1, I, pp. 1, 2; II, pp. 160, 163, 164; III, p. 594. The distinction between constituents and particles is made in Brown and Rechenberg, op. cit., note 1.
22. 8 E.g. Heisenberg, op. cit., note 1, I, pp. 1, 2; II, pp. 160, 163, 164; III, p. 594. The distinction between constituents and particles is made in Brown and Rechenberg, op. cit., note 1.
23. 9 Heisenberg, op. cit., note 1, III, p. 595.
24. 10 Cf. Bromberg, op. cit., note 1, pp. 309, 333-338; Miller, 'Heisenberg', op. cit., note 1, pp. 63-65.
25. 10 Cf. Bromberg, op. cit., note 1, pp. 309, 333-338; Miller, 'Heisenberg', op. cit., note 1, pp. 63-65.
26. 2, with its two protons and two electrons; however, Heisenberg did not stress the exchange origin here and called the neutron-neutron interaction a generic attractive Wechselwirkungsenergie. In the third paper (Heisenberg, op. cit., note 1, III, pp. 217-218) a 'static' neutron-proton interaction was added to that given in the first paper.
27. 12 Heisenberg, op. cit., note 1, I, p. 2.
28. 13 Cf. Brown, op. cit., note 1, p. 118; Miller, 'Heisenberg', op. cit., note 1, p. 65.
29. 13 Cf. Brown, op. cit., note 1, p. 118; Miller, 'Heisenberg', op. cit., note 1, p. 65.
30. 14 W. Heisenberg, 'Über den Bau der Atomkerne', manuscript, Werner-Heisenberg-Archiv, Munich.
31. 15 H. Bethe, 'Quantenmechanik der Ein-und Zwei-Elektronenprobleme', in H. Geiger and Karl Scheel (eds), Handbuch der Physik, Vol. 24, Part 1, Quantentheorie (Berlin: Julius Springer, 1933), pp. 273-560, see p. 529. I am not arguing that this terminological distinction was universally made at the time, only that it was available. Besides Bethe, Hideki Yukawa also identified Heisenberg's Austausch-Platzwechsel distinction with the distinction between the hydrogen molecule and the molecular ion; see Hideki Yukawa, 'The Roles of the Electron for Nuclear Structure', translated into English, along with other material from the Yukawa archives, in Rokuo Kawabe, 'Yukawa's First Two Talks', in Laurie M. Brown, Rokuo Kawabe, Michiji Konuma and Ziro Maki (eds), Elementary Particle Theory in Japan, 1935-1960 (Kyoto, 1988), pp. 149-175, see pp. 160-162.
32. 15 H. Bethe, 'Quantenmechanik der Ein-und Zwei-Elektronenprobleme', in H. Geiger and Karl Scheel (eds), Handbuch der Physik, Vol. 24, Part 1, Quantentheorie (Berlin: Julius Springer, 1933), pp. 273-560, see p. 529. I am not arguing that this terminological distinction was universally made at the time, only that it was available. Besides Bethe, Hideki Yukawa also identified Heisenberg's Austausch-Platzwechsel distinction with the distinction between the hydrogen molecule and the molecular ion; see Hideki Yukawa, 'The Roles of the Electron for Nuclear Structure', translated into English, along with other material from the Yukawa archives, in Rokuo Kawabe, 'Yukawa's First Two Talks', in Laurie M. Brown, Rokuo Kawabe, Michiji Konuma and Ziro Maki (eds), Elementary Particle Theory in Japan, 1935-1960 (Kyoto, 1988), pp. 149-175, see pp. 160-162.
33. 15 H. Bethe, 'Quantenmechanik der Ein-und Zwei-Elektronenprobleme', in H. Geiger and Karl Scheel (eds), Handbuch der Physik, Vol. 24, Part 1, Quantentheorie (Berlin: Julius Springer, 1933), pp. 273-560, see p. 529. I am not arguing that this terminological distinction was universally made at the time, only that it was available. Besides Bethe, Hideki Yukawa also identified Heisenberg's Austausch-Platzwechsel distinction with the distinction between the hydrogen molecule and the molecular ion; see Hideki Yukawa, 'The Roles of the Electron for Nuclear Structure', translated into English, along with other material from the Yukawa archives, in Rokuo Kawabe, 'Yukawa's First Two Talks', in Laurie M. Brown, Rokuo Kawabe, Michiji Konuma and Ziro Maki (eds), Elementary Particle Theory in Japan, 1935-1960 (Kyoto, 1988), pp. 149-175, see pp. 160-162.
34. 16 Heisenberg was likely familiar with the molecular ion, as Edward Teller had written his dissertation for him on that subject: Eduard Teller, 'Über das Wasserstoffmolekülion', Zeitschrift für Physik 61 (1930), 458-480.
35. 17 This concern was only strengthened by Heisenberg's hesitations about applying quantum mechanical ideas too literally in this new field.
36. 18 Cf. Miller, 'Theories', op. cit., note 1; Miller, 'Redefining', op. cit., note 1.
37. 18 Cf. Miller, 'Theories', op. cit., note 1; Miller, 'Redefining', op. cit., note 1.
38. 19 See the influential review by H. A. Bethe and R. F. Bacher, 'Nuclear Physics: A. Stationary States of Nuclei', Reviews of Modern Physics 8 (1936), 82-229, see pp. 93-95.
39. 20 See e.g. F. London, 'Über den Mechanismus der homöopolaren Bindung', in P. Debye (ed.), Probleme der modernen Physik: Arnold Sommerfeld zum 60. Geburtstag, (Leipzig: S. Hirzel, 1928), pp. 104-113. Moreover, to invoke saturation with Bose electrons (and thus without the exclusion principle), Heisenberg would have had to argue the point at considerable length, which he did not; I thank David Kaiser for pointing this out to me. Of course, the exchange approach was not the only way to explain chemical bonding. The molecular orbital approach to bonding, which was associated with Friedrich Hund and Robert Mulliken, did not rely on the exchange concept at all.
40. 21 W. Heisenberg, 'Die Struktur der leichten Atomkerne', Zeitschrift für Physik 96 (1935), 473-484; Ettore Majorana, 'Über die Kerntheorie', Zeitschrift für Physik 82 (1933), 137-145.
41. 21 W. Heisenberg, 'Die Struktur der leichten Atomkerne', Zeitschrift für Physik 96 (1935), 473-484; Ettore Majorana, 'Über die Kerntheorie', Zeitschrift für Physik 82 (1933), 137-145.
42. 22 G. C. Wick, 'Über die Wechselwirkung zwischen Neutronen und Protonen', Zeitschrift für Physik 84 (1933), 799-800.
43. 23 Heisenberg hid the electrons by introducing an additional variable for each heavy particle, the ρ-spin, that let him write the neutron-proton potential with a factor switching their positions. Here he built on Dirac's representation of permutations as products of spin matrices, which, although likely familiar to him from his work on ferromagnetism, was not very common at this time. That the ρ-coordinate thoroughly puzzled his contemporaries can be concluded from the jokes in the special issue (11 December 1932) of the Nachrichten of the Gesellschaft der Wissenschaften zu Göttingen, reprinted in Physikalische Blätter 17 (1961), 187. On the development of the ρ-coordinate see G. Rasche, 'Zur Geschichte des Begriffes "Isospin"', Archive for History of Exact Sciences 7 (1971), 257-276; Laurie M. Brown, 'Remarks on the History of Isospin', in Klaus Winter (ed.), Festi-Val: Festschrift for Val Telegdi, Essays in Physics in Honour of His 65th Birthday (Amsterdam: Elsevier, 1988), pp. 39-47. Although isospin was later used to represent the neutron and proton as two states of the same particle (and in this sense as identical particles), this idea was not yet expressed in Heisenberg's 1932-33 papers; as discussed above, at this stage Heisenberg depicted the proton as an elementary particle and the neutron as a compound.
44. 23 Heisenberg hid the electrons by introducing an additional variable for each heavy particle, the ρ-spin, that let him write the neutron-proton potential with a factor switching their positions. Here he built on Dirac's representation of permutations as products of spin matrices, which, although likely familiar to him from his work on ferromagnetism, was not very common at this time. That the ρ-coordinate thoroughly puzzled his contemporaries can be concluded from the jokes in the special issue (11 December 1932) of the Nachrichten of the Gesellschaft der Wissenschaften zu Göttingen, reprinted in Physikalische Blätter 17 (1961), 187. On the development of the ρ-coordinate see G. Rasche, 'Zur Geschichte des Begriffes "Isospin"', Archive for History of Exact Sciences 7 (1971), 257-276; Laurie M. Brown, 'Remarks on the History of Isospin', in Klaus Winter (ed.), Festi-Val: Festschrift for Val Telegdi, Essays in Physics in Honour of His 65th Birthday (Amsterdam: Elsevier, 1988), pp. 39-47. Although isospin was later used to represent the neutron and proton as two states of the same particle (and in this sense as identical particles), this idea was not yet expressed in Heisenberg's 1932-33 papers; as discussed above, at this stage Heisenberg depicted the proton as an elementary particle and the neutron as a compound.
45. 23 Heisenberg hid the electrons by introducing an additional variable for each heavy particle, the ρ-spin, that let him write the neutron-proton potential with a factor switching their positions. Here he built on Dirac's representation of permutations as products of spin matrices, which, although likely familiar to him from his work on ferromagnetism, was not very common at this time. That the ρ-coordinate thoroughly puzzled his contemporaries can be concluded from the jokes in the special issue (11 December 1932) of the Nachrichten of the Gesellschaft der Wissenschaften zu Göttingen, reprinted in Physikalische Blätter 17 (1961), 187. On the development of the ρ-coordinate see G. Rasche, 'Zur Geschichte des Begriffes "Isospin"', Archive for History of Exact Sciences 7 (1971), 257-276; Laurie M. Brown, 'Remarks on the History of Isospin', in Klaus Winter (ed.), Festi-Val: Festschrift for Val Telegdi, Essays in Physics in Honour of His 65th Birthday (Amsterdam: Elsevier, 1988), pp. 39-47. Although isospin was later used to represent the neutron and proton as two states of the same particle (and in this sense as identical particles), this idea was not yet expressed in Heisenberg's 1932-33 papers; as discussed above, at this stage Heisenberg depicted the proton as an elementary particle and the neutron as a compound.
46. 24 In the last paper Heisenberg in fact referred to the pairwise interactions J(r) as the Austauschglieder. Heisenberg, op. cit., note 1, III, p. 594.
47. 25 E. Amaldi, 'Ettore Majorana, Man and Scientist', in A. Zichichi (ed.), Strong and Weak Interactions: Present Problems (New York: Academic Press, 1966), pp. 9-77, see pp. 30-32.
48. 26 Majorana, op. cit., note 21, which was submitted from Heisenberg's institute and expresses thanks to him for suggestions. Cf. Dirac's comments on Heisenberg's report at the 1934 Solvay Conference: Structure et propriétés des noyaux atomiques: Rapports et discussion du septième conseil de physique. Institut International de Physique Solvay (Paris: Gauthier-Villars, 1934), pp. 330-331.
49. 26 Majorana, op. cit., note 21, which was submitted from Heisenberg's institute and expresses thanks to him for suggestions. Cf. Dirac's comments on Heisenberg's report at the 1934 Solvay Conference: Structure et propriétés des noyaux atomiques: Rapports et discussion du septième conseil de physique. Institut International de Physique Solvay (Paris: Gauthier-Villars, 1934), pp. 330-331.
50. 27 Ettore Majorana, 'Sulla formazione dello ione molecolare di He', Nuovo Cimento 8 (1931), 22-28; reprinted in La vita e l'opera di Ettore Majorana (Rome: Accademia Nazionale dei Lincei, 1966), pp. 9-15.
51. 27 Ettore Majorana, 'Sulla formazione dello ione molecolare di He', Nuovo Cimento 8 (1931), 22-28; reprinted in La vita e l'opera di Ettore Majorana (Rome: Accademia Nazionale dei Lincei, 1966), pp. 9-15.
52. 28 Edward Teller also explained the exchange force in terms of energetic degeneracy in his 1933 review 'γ-Strahlung und Kernzertrümmerung' in Eucken, Lummer and Waetzmann (eds), op. cit., note 3, p. 577, 2. It is interesting that Teller, like Majorana, had cut his teeth on problems involving molecular ions, for which this sort of conception was more helpful than for neutral molecules.
53. 29 See e.g. op. cit., note 19, Sections 7, 9-12.
54. 30 Cf. Rudolf Peierls, 'The Development of Our Ideas on the Nuclear Forces', in Roger H. Stuewer (ed.), Nuclear Physics in Retrospect: Proceedings of a Symposium on the 1930s (Minneapolis: University of Minnesota Press, 1979), pp. 183-202.
55. 31 By pointing out the unavailability of the QED analogy for the exchange nature of forces I do not call into question other aspects of the analogizing of field theories of nuclear forces to QED, as cited in much of the historiographical literature and laid out in Olivier Darrigol, 'The Quantum Electrodynamical Analogy in Early Nuclear Theory or The Roots of Yukawa's Theory', Revue d'Histoire des Sciences 41 (1988), 225-297. For another instance of nuclear physics taking the lead, see David Kaiser, 'Niels Bohr's Conceptual Legacy in Contemporary Particle Physics', in Jan Faye and Henry J. Folse (eds), Niels Bohr and Contemporary Philosophy (Dordrecht: Kluwer, 1994), pp. 257-268.
56. 31 By pointing out the unavailability of the QED analogy for the exchange nature of forces I do not call into question other aspects of the analogizing of field theories of nuclear forces to QED, as cited in much of the historiographical literature and laid out in Olivier Darrigol, 'The Quantum Electrodynamical Analogy in Early Nuclear Theory or The Roots of Yukawa's Theory', Revue d'Histoire des Sciences 41 (1988), 225-297. For another instance of nuclear physics taking the lead, see David Kaiser, 'Niels Bohr's Conceptual Legacy in Contemporary Particle Physics', in Jan Faye and Henry J. Folse (eds), Niels Bohr and Contemporary Philosophy (Dordrecht: Kluwer, 1994), pp. 257-268.
57. 32 W. Heisenberg and W. Pauli, 'Zur Quantendynamik der Wellenfelder', Zeitschrift für Physik 56 (1929), 1-61; W. Heisenberg and W. Pauli, 'Zur Quantentheorie der Wellenfelder, II', Zeitschrift für Physik 59 (1930), 168-190.
58. 32 W. Heisenberg and W. Pauli, 'Zur Quantendynamik der Wellenfelder', Zeitschrift für Physik 56 (1929), 1-61; W. Heisenberg and W. Pauli, 'Zur Quantentheorie der Wellenfelder, II', Zeitschrift für Physik 59 (1930), 168-190.
59. 33 See also O. Darrigol, 'La genèse du concept de champ quantique', Annales de Physique 9 (1984), 433-501; O. Darrigol, 'The Origin of Quantized Matter Waves', Historical Studies in the Physical and Biological Sciences 16(2) (1986), 197-253.
60. 33 See also O. Darrigol, 'La genèse du concept de champ quantique', Annales de Physique 9 (1984), 433-501; O. Darrigol, 'The Origin of Quantized Matter Waves', Historical Studies in the Physical and Biological Sciences 16(2) (1986), 197-253.
61. 34 P. A. M. Dirac, 'The Quantum Theory of the Emission and Absorption of Radiation', Proceedings of the Royal Society of London A 114 (1927), 243-265; P. A. M. Dirac, 'The Quantum Theory of Dispersion', Proceedings of the Royal Society of London A 114 (1927), 710-728; P. Jordan and W. Pauli, 'Zur Quantenelektrodynamik ladungsfreier Felder', Zeitschrift für Physik 47 (1928), 151-173.
62. 34 P. A. M. Dirac, 'The Quantum Theory of the Emission and Absorption of Radiation', Proceedings of the Royal Society of London A 114 (1927), 243-265; P. A. M. Dirac, 'The Quantum Theory of Dispersion', Proceedings of the Royal Society of London A 114 (1927), 710-728; P. Jordan and W. Pauli, 'Zur Quantenelektrodynamik ladungsfreier Felder', Zeitschrift für Physik 47 (1928), 151-173.
63. 34 P. A. M. Dirac, 'The Quantum Theory of the Emission and Absorption of Radiation', Proceedings of the Royal Society of London A 114 (1927), 243-265; P. A. M. Dirac, 'The Quantum Theory of Dispersion', Proceedings of the Royal Society of London A 114 (1927), 710-728; P. Jordan and W. Pauli, 'Zur Quantenelektrodynamik ladungsfreier Felder', Zeitschrift für Physik 47 (1928), 151-173.
64. 35 The language here is somewhat confusing, as Φ is not really a scalar, but rather the time-component of a four-vector.
65. 36 Heisenberg and Pauli, op. cit., note 32, I, p. 30.
66. 37 The corresponding requirements for the total momentum, spin and other properties of the field were not considered here.
67. 38 Like ε, δ was to be sent to zero in the end, and its sole function was to keep the oscillators from becoming non-periodic in the meantime. Fortunately, Heisenberg and Pauli noted, the unperiodic solutions for the potentials corresponded to periodic solutions for the actual field strengths, and solutions for the field strengths which went to zero with ε in the bargain. Heisenberg and Pauli, op. cit., note 32, I, p. 45.
68. 39 Ibid., p. 52, Eq. 112.
69. 40 L. Rosenfeld, 'Über die longitudinalen Eigenlösungen der Heisenberg-Paulischen elektromagnetischen Gleichungen', Zeitschrift für Physik 58 (1929), 540-555. This paper is interesting not because it was so influential, but because it explicitly addressed the question of the four polarizations.
70. 41 Although Heisenberg and Pauli noted that the solutions for λ=3, 4 gave unphysical contributions to the probability of certain processes involving photon emission, they did not discuss the root of the difference here between λ=1, 2 and λ=3, 4. Heisenberg and Pauli, op. cit., note 32, I, p. 59.
71. 42 Rosenfeld thereby showed that '"normal" light quanta', or transversely polarized photons, played no role in the Coulomb interaction. Rosenfeld, op. cit., note 40, p. 548.
72. 43 Ibid., pp. 552-553.
73. 44 This necessity arose because only three of the four Maxwell equations could be derived variationally from a field Lagrangian with no Φ; the fourth, divE - ρ=0, was no longer guaranteed to be satisfied. Heisenberg and Pauli therefore imposed this equation, expressed in terms of field operators, as a supplementary condition on the wave function. The possibility of doing so was ensured by the remaining freedom in the choice of gauge.
74. 45 J. R. Oppenheimer, 'Note on the Theory of the Interaction of Field and Matter', Physical Review 35 (1930), 466-477; Oppenheimer's method was essentially to perform a canonical transformation on the states and variables of the system. E. Fermi, 'Sopra l'elettrodinamica quantistica', Rendiconti dell'Accademia dei Lincei 9 (1929), 881-887; E. Fermi, 'Sopra l'elettrodinamica quantistica, Nota II', Rendiconti dell'Accademia dei Lincei 12 (1930), 431-435; and the influential article by E. Fermi, 'Quantum Theory of Radiation', Reviews of Modern Physics 4 (1932), 87-132. Fermi simply wrote down a Hamiltonian for the system and verified that it reproduced the equations for the Fourier components of the electromagnetic field in the Lorentz gauge. Although the field Hamiltonian contained the time-like oscillators with a negative sign, he did not comment on this. See also S. S. Schweber, QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga (Princeton: Princeton University Press, 1994), pp. 72-75.
75. 45 J. R. Oppenheimer, 'Note on the Theory of the Interaction of Field and Matter', Physical Review 35 (1930), 466-477; Oppenheimer's method was essentially to perform a canonical transformation on the states and variables of the system. E. Fermi, 'Sopra l'elettrodinamica quantistica', Rendiconti dell'Accademia dei Lincei 9 (1929), 881-887; E. Fermi, 'Sopra l'elettrodinamica quantistica, Nota II', Rendiconti dell'Accademia dei Lincei 12 (1930), 431-435; and the influential article by E. Fermi, 'Quantum Theory of Radiation', Reviews of Modern Physics 4 (1932), 87-132. Fermi simply wrote down a Hamiltonian for the system and verified that it reproduced the equations for the Fourier components of the electromagnetic field in the Lorentz gauge. Although the field Hamiltonian contained the time-like oscillators with a negative sign, he did not comment on this. See also S. S. Schweber, QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga (Princeton: Princeton University Press, 1994), pp. 72-75.
76. 45 J. R. Oppenheimer, 'Note on the Theory of the Interaction of Field and Matter', Physical Review 35 (1930), 466-477; Oppenheimer's method was essentially to perform a canonical transformation on the states and variables of the system. E. Fermi, 'Sopra l'elettrodinamica quantistica', Rendiconti dell'Accademia dei Lincei 9 (1929), 881-887; E. Fermi, 'Sopra l'elettrodinamica quantistica, Nota II', Rendiconti dell'Accademia dei Lincei 12 (1930), 431-435; and the influential article by E. Fermi, 'Quantum Theory of Radiation', Reviews of Modern Physics 4 (1932), 87-132. Fermi simply wrote down a Hamiltonian for the system and verified that it reproduced the equations for the Fourier components of the electromagnetic field in the Lorentz gauge. Although the field Hamiltonian contained the time-like oscillators with a negative sign, he did not comment on this. See also S. S. Schweber, QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga (Princeton: Princeton University Press, 1994), pp. 72-75.
77. 45 J. R. Oppenheimer, 'Note on the Theory of the Interaction of Field and Matter', Physical Review 35 (1930), 466-477; Oppenheimer's method was essentially to perform a canonical transformation on the states and variables of the system. E. Fermi, 'Sopra l'elettrodinamica quantistica', Rendiconti dell'Accademia dei Lincei 9 (1929), 881-887; E. Fermi, 'Sopra l'elettrodinamica quantistica, Nota II', Rendiconti dell'Accademia dei Lincei 12 (1930), 431-435; and the influential article by E. Fermi, 'Quantum Theory of Radiation', Reviews of Modern Physics 4 (1932), 87-132. Fermi simply wrote down a Hamiltonian for the system and verified that it reproduced the equations for the Fourier components of the electromagnetic field in the Lorentz gauge. Although the field Hamiltonian contained the time-like oscillators with a negative sign, he did not comment on this. See also S. S. Schweber, QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga (Princeton: Princeton University Press, 1994), pp. 72-75.
78. 45 J. R. Oppenheimer, 'Note on the Theory of the Interaction of Field and Matter', Physical Review 35 (1930), 466-477; Oppenheimer's method was essentially to perform a canonical transformation on the states and variables of the system. E. Fermi, 'Sopra l'elettrodinamica quantistica', Rendiconti dell'Accademia dei Lincei 9 (1929), 881-887; E. Fermi, 'Sopra l'elettrodinamica quantistica, Nota II', Rendiconti dell'Accademia dei Lincei 12 (1930), 431-435; and the influential article by E. Fermi, 'Quantum Theory of Radiation', Reviews of Modern Physics 4 (1932), 87-132. Fermi simply wrote down a Hamiltonian for the system and verified that it reproduced the equations for the Fourier components of the electromagnetic field in the Lorentz gauge. Although the field Hamiltonian contained the time-like oscillators with a negative sign, he did not comment on this. See also S. S. Schweber, QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga (Princeton: Princeton University Press, 1994), pp. 72-75.
79. 46 For instance, L. Rosenfeld, 'La théorie quantique des champs', Annales de l'Institut Henri Poincaré 2 (1931), 25-91; G. Breit, 'Quantum Theory of Dispersion', Reviews of Modern Physics 4 (1932), 504-576; W. Pauli, 'Die allgemeinen Prinzipien der Wellenmechanik', in Geiger and Scheel (eds), op. cit., note 15, pp. 83-272; Gregor Wentzel, 'Wellenmechanik der Stoß-und Strahlungsvorgänge', ibid., pp. 695-784; W. Heitler, The Quantum Theory of Radiation (Oxford: Oxford University Press, 1936); H. A. Kramers, 'Die Grundlagen der Quantentheorie und Quantentheorie des Elektrons und der Strahlung', in A. Eucken and K. L. Wolf (eds), Hand-und Jahrbuch der chemischen Physik, Vol. 1, Theorie des Aufbaues der Materie (Leipzig: Akademische Verlagsgesellschaft, 1938); Gregor Wentzel, Einführung in die Quantentheorie der Wellenfelder (Wien: Franz Deuticke, 1943).
80. 46 For instance, L. Rosenfeld, 'La théorie quantique des champs', Annales de l'Institut Henri Poincaré 2 (1931), 25-91; G. Breit, 'Quantum Theory of Dispersion', Reviews of Modern Physics 4 (1932), 504-576; W. Pauli, 'Die allgemeinen Prinzipien der Wellenmechanik', in Geiger and Scheel (eds), op. cit., note 15, pp. 83-272; Gregor Wentzel, 'Wellenmechanik der Stoß-und Strahlungsvorgänge', ibid., pp. 695-784; W. Heitler, The Quantum Theory of Radiation (Oxford: Oxford University Press, 1936); H. A. Kramers, 'Die Grundlagen der Quantentheorie und Quantentheorie des Elektrons und der Strahlung', in A. Eucken and K. L. Wolf (eds), Hand-und Jahrbuch der chemischen Physik, Vol. 1, Theorie des Aufbaues der Materie (Leipzig: Akademische Verlagsgesellschaft, 1938); Gregor Wentzel, Einführung in die Quantentheorie der Wellenfelder (Wien: Franz Deuticke, 1943).
81. 46 For instance, L. Rosenfeld, 'La théorie quantique des champs', Annales de l'Institut Henri Poincaré 2 (1931), 25-91; G. Breit, 'Quantum Theory of Dispersion', Reviews of Modern Physics 4 (1932), 504-576; W. Pauli, 'Die allgemeinen Prinzipien der Wellenmechanik', in Geiger and Scheel (eds), op. cit., note 15, pp. 83-272; Gregor Wentzel, 'Wellenmechanik der Stoß-und Strahlungsvorgänge', ibid., pp. 695-784; W. Heitler, The Quantum Theory of Radiation (Oxford: Oxford University Press, 1936); H. A. Kramers, 'Die Grundlagen der Quantentheorie und Quantentheorie des Elektrons und der Strahlung', in A. Eucken and K. L. Wolf (eds), Hand-und Jahrbuch der chemischen Physik, Vol. 1, Theorie des Aufbaues der Materie (Leipzig: Akademische Verlagsgesellschaft, 1938); Gregor Wentzel, Einführung in die Quantentheorie der Wellenfelder (Wien: Franz Deuticke, 1943).
82. 46 For instance, L. Rosenfeld, 'La théorie quantique des champs', Annales de l'Institut Henri Poincaré 2 (1931), 25-91; G. Breit, 'Quantum Theory of Dispersion', Reviews of Modern Physics 4 (1932), 504-576; W. Pauli, 'Die allgemeinen Prinzipien der Wellenmechanik', in Geiger and Scheel (eds), op. cit., note 15, pp. 83-272; Gregor Wentzel, 'Wellenmechanik der Stoß-und Strahlungsvorgänge', ibid., pp. 695-784; W. Heitler, The Quantum Theory of Radiation (Oxford: Oxford University Press, 1936); H. A. Kramers, 'Die Grundlagen der Quantentheorie und Quantentheorie des Elektrons und der Strahlung', in A. Eucken and K. L. Wolf (eds), Hand-und Jahrbuch der chemischen Physik, Vol. 1, Theorie des Aufbaues der Materie (Leipzig: Akademische Verlagsgesellschaft, 1938); Gregor Wentzel, Einführung in die Quantentheorie der Wellenfelder (Wien: Franz Deuticke, 1943).
83. 46 For instance, L. Rosenfeld, 'La théorie quantique des champs', Annales de l'Institut Henri Poincaré 2 (1931), 25-91; G. Breit, 'Quantum Theory of Dispersion', Reviews of Modern Physics 4 (1932), 504-576; W. Pauli, 'Die allgemeinen Prinzipien der Wellenmechanik', in Geiger and Scheel (eds), op. cit., note 15, pp. 83-272; Gregor Wentzel, 'Wellenmechanik der Stoß-und Strahlungsvorgänge', ibid., pp. 695-784; W. Heitler, The Quantum Theory of Radiation (Oxford: Oxford University Press, 1936); H. A. Kramers, 'Die Grundlagen der Quantentheorie und Quantentheorie des Elektrons und der Strahlung', in A. Eucken and K. L. Wolf (eds), Hand-und Jahrbuch der chemischen Physik, Vol. 1, Theorie des Aufbaues der Materie (Leipzig: Akademische Verlagsgesellschaft, 1938); Gregor Wentzel, Einführung in die Quantentheorie der Wellenfelder (Wien: Franz Deuticke, 1943).
84. 46 For instance, L. Rosenfeld, 'La théorie quantique des champs', Annales de l'Institut Henri Poincaré 2 (1931), 25-91; G. Breit, 'Quantum Theory of Dispersion', Reviews of Modern Physics 4 (1932), 504-576; W. Pauli, 'Die allgemeinen Prinzipien der Wellenmechanik', in Geiger and Scheel (eds), op. cit., note 15, pp. 83-272; Gregor Wentzel, 'Wellenmechanik der Stoß-und Strahlungsvorgänge', ibid., pp. 695-784; W. Heitler, The Quantum Theory of Radiation (Oxford: Oxford University Press, 1936); H. A. Kramers, 'Die Grundlagen der Quantentheorie und Quantentheorie des Elektrons und der Strahlung', in A. Eucken and K. L. Wolf (eds), Hand-und Jahrbuch der chemischen Physik, Vol. 1, Theorie des Aufbaues der Materie (Leipzig: Akademische Verlagsgesellschaft, 1938); Gregor Wentzel, Einführung in die Quantentheorie der Wellenfelder (Wien: Franz Deuticke, 1943).
85. 46 For instance, L. Rosenfeld, 'La théorie quantique des champs', Annales de l'Institut Henri Poincaré 2 (1931), 25-91; G. Breit, 'Quantum Theory of Dispersion', Reviews of Modern Physics 4 (1932), 504-576; W. Pauli, 'Die allgemeinen Prinzipien der Wellenmechanik', in Geiger and Scheel (eds), op. cit., note 15, pp. 83-272; Gregor Wentzel, 'Wellenmechanik der Stoß-und Strahlungsvorgänge', ibid., pp. 695-784; W. Heitler, The Quantum Theory of Radiation (Oxford: Oxford University Press, 1936); H. A. Kramers, 'Die Grundlagen der Quantentheorie und Quantentheorie des Elektrons und der Strahlung', in A. Eucken and K. L. Wolf (eds), Hand-und Jahrbuch der chemischen Physik, Vol. 1, Theorie des Aufbaues der Materie (Leipzig: Akademische Verlagsgesellschaft, 1938); Gregor Wentzel, Einführung in die Quantentheorie der Wellenfelder (Wien: Franz Deuticke, 1943).
86. 47 Heitler, op. cit., note 46, p. 66. Here Heitler was describing the general four-component field in vacuum, but the same idea is present in his discussion of the field in interaction with charges. It may also be noted that photons whose energy and momentum do not form a four-vector (photons that are 'off the mass shell') are allowed today in QED, but only in virtual processes; this is another way of understanding Feynman's contribution (see below).
87. 48 See the works cited in note 46. The one apparent exception is Wentzel's 1943 textbook, op. cit., note 46, pp. 189-190, where a picture of the electron-electron interaction by means of 'wechselseitig emittierte und absorbierte' photons (p. 190) is used as an analogy for the photon-photon interaction by means of virtual electron-positron pairs. Curiously, the picture of photon exchange is not present in the earlier sections on the electromagnetic field, which follow the usual approach of eliminating the non-transverse variables.
88. 49 P. A. M. Dirac, 'Relativistic Quantum mechanics', Proceedings of the Royal Society of London A 136 (1932), 453-464. Although Dirac thought he was creating an alternative to the Heisenberg-Pauli QED, essentially he was suggesting the use of the interaction representation. See L. Rosenfeld, 'Über eine mögliche Fassung des Diracschen Programms zur Quantenelektrodynamik und deren formalen Zusammenhang mit der Heisenberg-Paulischen Theorie', Zeitschrift für Physik 76 (1932), 729-734; P. A. M. Dirac, V. A. Fock and B. Podolsky, 'On Quantum Electrodynamics', Physikalische Zeitschrift der Sowjetunion 2 (1932), 468-479.
89. 49 P. A. M. Dirac, 'Relativistic Quantum mechanics', Proceedings of the Royal Society of London A 136 (1932), 453-464. Although Dirac thought he was creating an alternative to the Heisenberg-Pauli QED, essentially he was suggesting the use of the interaction representation. See L. Rosenfeld, 'Über eine mögliche Fassung des Diracschen Programms zur Quantenelektrodynamik und deren formalen Zusammenhang mit der Heisenberg-Paulischen Theorie', Zeitschrift für Physik 76 (1932), 729-734; P. A. M. Dirac, V. A. Fock and B. Podolsky, 'On Quantum Electrodynamics', Physikalische Zeitschrift der Sowjetunion 2 (1932), 468-479.
90. 49 P. A. M. Dirac, 'Relativistic Quantum mechanics', Proceedings of the Royal Society of London A 136 (1932), 453-464. Although Dirac thought he was creating an alternative to the Heisenberg-Pauli QED, essentially he was suggesting the use of the interaction representation. See L. Rosenfeld, 'Über eine mögliche Fassung des Diracschen Programms zur Quantenelektrodynamik und deren formalen Zusammenhang mit der Heisenberg-Paulischen Theorie', Zeitschrift für Physik 76 (1932), 729-734; P. A. M. Dirac, V. A. Fock and B. Podolsky, 'On Quantum Electrodynamics', Physikalische Zeitschrift der Sowjetunion 2 (1932), 468-479.
91. 50 V. A. Fock and B. Podolsky, 'On the Quantization of Electro-Magnetic Waves and the Interaction of Charges on Dirac's Theory', Physikalische Zeitschrift der Sowjetunion 1 (1932), 801-817.
92. 51 Their Lagrangian, or equivalently Rosenfeld's, was generally taken to be 'Fermi's Lagrangian' for the radiation field, although Fermi did not himself write down a Lagrangian. See also Heisenberg and Pauli, op. cit., note 32, I, p. 171 (footnote).
93. 52 Rosenfeld, op. cit., note 49, p. 733; see also V. Fock, 'Zur Quantenelektrodynamik', Physikalische Zeitschrift der Sowjetunion 6 (1934), 425-469.
94. 52 Rosenfeld, op. cit., note 49, p. 733; see also V. Fock, 'Zur Quantenelektrodynamik', Physikalische Zeitschrift der Sowjetunion 6 (1934), 425-469.
95. 53 P. A. M. Dirac, The Principles of Quantum Mechanics, 2nd edn (Oxford: Oxford University Press, 1935).
96. 54 H. Bethe and E. Fermi, 'Über die Wechselwirkung von zwei Elektronen', Zeitschrift für Physik 77 (1932), 296-306.
97. 55 G. Breit, 'The Effect of Retardation on the Interaction of Two Electrons', Physical Review 34 (1929), 553-573; G. Breit, 'The Fine Structure of He as a Test of the Spin Interactions of Two Electrons', Physical Review 36 (1930), 383-397; G. Breit, 'Dirac's Equation and the Spin-Spin Interactions of Two Electrons', Physical Review 39 (1932), 616-624.
98. 55 G. Breit, 'The Effect of Retardation on the Interaction of Two Electrons', Physical Review 34 (1929), 553-573; G. Breit, 'The Fine Structure of He as a Test of the Spin Interactions of Two Electrons', Physical Review 36 (1930), 383-397; G. Breit, 'Dirac's Equation and the Spin-Spin Interactions of Two Electrons', Physical Review 39 (1932), 616-624.
99. 55 G. Breit, 'The Effect of Retardation on the Interaction of Two Electrons', Physical Review 34 (1929), 553-573; G. Breit, 'The Fine Structure of He as a Test of the Spin Interactions of Two Electrons', Physical Review 36 (1930), 383-397; G. Breit, 'Dirac's Equation and the Spin-Spin Interactions of Two Electrons', Physical Review 39 (1932), 616-624.
100. 56 C. Møller, 'Über den Stoß zweier Teilchen unter Berücksichtigung der Retardation der Kräfte', Zeitschrift für Physik 70 (1931), 786-795; cf. L. Rosenfeld, 'Bemerkung zur korrespondenzmäßigen Behandlung des relativistischen Mehrkörperproblems', Zeitschrift für Physik 73 (1931), 253-259. On Møller's contributions and their context see also Helge Kragh, 'Relativistic Collisions: The Work of Christian Møller in the Early 1930s', Archive for History of Exact Sciences 43 (1992), 299-328; and Xavier Roqué, 'Møller Scattering: A Neglected Application of Early Quantum Electrodynamics', Archive for History of Exact Sciences 44 (1992), 197-264.
101. 56 C. Møller, 'Über den Stoß zweier Teilchen unter Berücksichtigung der Retardation der Kräfte', Zeitschrift für Physik 70 (1931), 786-795; cf. L. Rosenfeld, 'Bemerkung zur korrespondenzmäßigen Behandlung des relativistischen Mehrkörperproblems', Zeitschrift für Physik 73 (1931), 253-259. On Møller's contributions and their context see also Helge Kragh, 'Relativistic Collisions: The Work of Christian Møller in the Early 1930s', Archive for History of Exact Sciences 43 (1992), 299-328; and Xavier Roqué, 'Møller Scattering: A Neglected Application of Early Quantum Electrodynamics', Archive for History of Exact Sciences 44 (1992), 197-264.
102. 56 C. Møller, 'Über den Stoß zweier Teilchen unter Berücksichtigung der Retardation der Kräfte', Zeitschrift für Physik 70 (1931), 786-795; cf. L. Rosenfeld, 'Bemerkung zur korrespondenzmäßigen Behandlung des relativistischen Mehrkörperproblems', Zeitschrift für Physik 73 (1931), 253-259. On Møller's contributions and their context see also Helge Kragh, 'Relativistic Collisions: The Work of Christian Møller in the Early 1930s', Archive for History of Exact Sciences 43 (1992), 299-328; and Xavier Roqué, 'Møller Scattering: A Neglected Application of Early Quantum Electrodynamics', Archive for History of Exact Sciences 44 (1992), 197-264.
103. 56 C. Møller, 'Über den Stoß zweier Teilchen unter Berücksichtigung der Retardation der Kräfte', Zeitschrift für Physik 70 (1931), 786-795; cf. L. Rosenfeld, 'Bemerkung zur korrespondenzmäßigen Behandlung des relativistischen Mehrkörperproblems', Zeitschrift für Physik 73 (1931), 253-259. On Møller's contributions and their context see also Helge Kragh, 'Relativistic Collisions: The Work of Christian Møller in the Early 1930s', Archive for History of Exact Sciences 43 (1992), 299-328; and Xavier Roqué, 'Møller Scattering: A Neglected Application of Early Quantum Electrodynamics', Archive for History of Exact Sciences 44 (1992), 197-264.
104. 57 In the Breit case, Bethe and Fermi worked with an arbitrary number of electrons and showed that the process via intermediate photon states gave rise to an interaction energy between all pairs of electrons, instead of just one particular pair.
105. 58 Because Bethe and Fermi, following Møller, worked in the Born approximation, the electrons were assumed to have definite momenta, and conservation of momentum could also be seen at each step of the process.
106. 59 E. Fermi, 'Tentativo di una teoria dell'emissione dei raggi "beta"', Ricerca Scientifica 4 (1933), 491-495; E. Fermi, 'Versuch einer Theorie der β-Strahlen, I', Zeitschrift für Physik 88 (1934), 161-177.
107. 59 E. Fermi, 'Tentativo di una teoria dell'emissione dei raggi "beta"', Ricerca Scientifica 4 (1933), 491-495; E. Fermi, 'Versuch einer Theorie der β-Strahlen, I', Zeitschrift für Physik 88 (1934), 161-177.
108. 60 Ig. Tamm, 'Exchange Forces between Neutrons and Protons, and Fermi's Theory', Nature 133 (1934), 981; D. Iwanenko, 'Interaction of Neutrons and Protons', Nature 133 (1934), 981-982. As discussed below, Heisenberg and Fermi reached the same conclusions as Tamm and Iwanenko but did not publish.
109. 60 Ig. Tamm, 'Exchange Forces between Neutrons and Protons, and Fermi's Theory', Nature 133 (1934), 981; D. Iwanenko, 'Interaction of Neutrons and Protons', Nature 133 (1934), 981-982. As discussed below, Heisenberg and Fermi reached the same conclusions as Tamm and Iwanenko but did not publish.
110. 61 Heisenberg to Pauli, 18 January 1934, in Wolfgang Pauli, Wissenschaftlicher Briefwechsel, K. von Meyenn (ed.), Vol. 2, 1930-1939 (New York: Springer, 1985), p. 250.
111. 62 Cf. The calculations in Fermi's notebook no. 16, January 1934, Archive for History of Quantum Physics.
112. 63 Fermi to Heisenberg, 30 January 1934, Archive for History of Quantum Physics.
113. 64 Heisenberg to Pauli, 8 February 1934, in op. cit., note 61, p. 281.
114. 65 Heisenberg to Bohr, 17 April 1934, Archive for History of Quantum Physics. The sort of 'korrespondenzmässige Analogie' that he outlined for Bohr also formed the introduction to his Cambridge lectures (see Heisenberg, 'Disposition der Vorträge in Cambridge', manuscript, Werner-Heisenberg-Archiv, Munich) and the subject of his contribution to the Zeeman Festschrift in 1935, where he discussed at length the common features linking the atomic and nuclear realms; W. Heisenberg, 'Bemerkungen zur Theorie des Atomkerns', in Zeeman Verhandelingen (The Hague: Martinus Nijhoff, 1935), pp. 108-116, see p. 108.
115. 65 Heisenberg to Bohr, 17 April 1934, Archive for History of Quantum Physics. The sort of 'korrespondenzmässige Analogie' that he outlined for Bohr also formed the introduction to his Cambridge lectures (see Heisenberg, 'Disposition der Vorträge in Cambridge', manuscript, Werner-Heisenberg-Archiv, Munich) and the subject of his contribution to the Zeeman Festschrift in 1935, where he discussed at length the common features linking the atomic and nuclear realms; W. Heisenberg, 'Bemerkungen zur Theorie des Atomkerns', in Zeeman Verhandelingen (The Hague: Martinus Nijhoff, 1935), pp. 108-116, see p. 108.
116. 66 Ibid., p. 240. A less developed version of this table is to be found in Heisenberg's letter to Bohr (op. cit., note 65).
117. 67 E.g. in a 1937 lecture, where Heisenberg went out of his way to interpose the field between the force and the mediator particle: 'Die gegenwärtigen Aufgaben der theoretischen Physik', Scientia 31 (1938), 61-69, on p. 67; reprinted in Heisenberg, Gesammelte Werkel Collected Works, Walter Blum, Hans-Peter Dürr and Helmut Rechenberg (eds), Vol. CI, Physik und Erkenntnis 1927-1955 (München: Piper, 1984), pp.-133-141.
118. 67 E.g. in a 1937 lecture, where Heisenberg went out of his way to interpose the field between the force and the mediator particle: 'Die gegenwärtigen Aufgaben der theoretischen Physik', Scientia 31 (1938), 61-69, on p. 67; reprinted in Heisenberg, Gesammelte Werkel Collected Works, Walter Blum, Hans-Peter Dürr and Helmut Rechenberg (eds), Vol. CI, Physik und Erkenntnis 1927-1955 (München: Piper, 1984), pp.-133-141.
119. 68 Iwanenko, op. cit., note 60; Tamm, op. cit., note 60; Ig. Tamm, 'Interaction of Neutrons and Protons', Nature 134 (1934), 1010-1011, is a little stricter in expression.
120. 68 Iwanenko, op. cit., note 60; Tamm, op. cit., note 60; Ig. Tamm, 'Interaction of Neutrons and Protons', Nature 134 (1934), 1010-1011, is a little stricter in expression.
121. 68 Iwanenko, op. cit., note 60; Tamm, op. cit., note 60; Ig. Tamm, 'Interaction of Neutrons and Protons', Nature 134 (1934), 1010-1011, is a little stricter in expression.
122. 69 D. Iwanenko and A. Sokolow, 'Zur Wechselwirkung der schweren Teilchen', Zeitschrift für Physik 102 (1936), 119-131, see p. 126.
123. 70 I am not suggesting this article was responsible for the development of the photon-exchange picture for QED, only that it was indicative of it. The same is true of the next case.
124. 71 C. F. v. Weizsäcker, 'Über die Spinabhängigkeit der Kernkräfte', Zeitschrift für Physik 102 (1936), 572-602, see p. 573 (the parenthesis is in the original); C. F. von Weizsäcker, Die Atomkerne: Grundlagen und Anwendungen ihrer Theorie (Leipzig: Akademische Verlagsgesellschaft, 1937).
125. 71 C. F. v. Weizsäcker, 'Über die Spinabhängigkeit der Kernkräfte', Zeitschrift für Physik 102 (1936), 572-602, see p. 573 (the parenthesis is in the original); C. F. von Weizsäcker, Die Atomkerne: Grundlagen und Anwendungen ihrer Theorie (Leipzig: Akademische Verlagsgesellschaft, 1937).
126. 72 C. F. v. Weizsäcker, 'Ausstrahlung bei Stößen sehr schneller Elektronen', Zeitschrift für Physik 88 (1934), 612-625; see also E. J. Williams, 'Correlation of Certain Collision Problems with Radiation Theory', Kongelige Danske Videnskabernes Selskab, Matematisk-fysiske Meddelelser 13(4) (1935). The Weizsäcker-Williams approach, which was developed for the collision of a high-energy electron with an atomic nucleus, calculated the radiation thereby emitted by treating the field of the nucleus (in the electron's rest frame) as apure radiation field composed of 'equivalent' photons, out of which photons could then be scattered according to the Klein-Nishina formula.
127. 72 C. F. v. Weizsäcker, 'Ausstrahlung bei Stößen sehr schneller Elektronen', Zeitschrift für Physik 88 (1934), 612-625; see also E. J. Williams, 'Correlation of Certain Collision Problems with Radiation Theory', Kongelige Danske Videnskabernes Selskab, Matematisk-fysiske Meddelelser 13(4) (1935). The Weizsäcker-Williams approach, which was developed for the collision of a high-energy electron with an atomic nucleus, calculated the radiation thereby emitted by treating the field of the nucleus (in the electron's rest frame) as apure radiation field composed of 'equivalent' photons, out of which photons could then be scattered according to the Klein-Nishina formula.
128. 73 For a review of developments in the mid-1950s, see Laurie M. Brown and Helmut Rechenberg, 'Field Theories of Nuclear Forces in the 1930s: The Fermi-Field Theory', Historical Studies in the Physical and Biological Sciences 25(1) (1994), 1-24.
129. 74 On Yukawa's work of 1933-38 see Laurie M. Brown, 'Yukawa's Prediction of the Meson', Centaurus 25 (1981), 71-132; Laurie M. Brown, 'How Yukawa Arrived at the Meson Theory', Progress of Theoretical Physics Supplement 85 (1985), 13-18; Laurie M. Brown, 'Yukawa in the 1930s: A Gentle Revolutionary', Historia Scientiarum 36 (1989), 1-21; Darrigol, op. cit., note 31.
130. 74 On Yukawa's work of 1933-38 see Laurie M. Brown, 'Yukawa's Prediction of the Meson', Centaurus 25 (1981), 71-132; Laurie M. Brown, 'How Yukawa Arrived at the Meson Theory', Progress of Theoretical Physics Supplement 85 (1985), 13-18; Laurie M. Brown, 'Yukawa in the 1930s: A Gentle Revolutionary', Historia Scientiarum 36 (1989), 1-21; Darrigol, op. cit., note 31.
131. 74 On Yukawa's work of 1933-38 see Laurie M. Brown, 'Yukawa's Prediction of the Meson', Centaurus 25 (1981), 71-132; Laurie M. Brown, 'How Yukawa Arrived at the Meson Theory', Progress of Theoretical Physics Supplement 85 (1985), 13-18; Laurie M. Brown, 'Yukawa in the 1930s: A Gentle Revolutionary', Historia Scientiarum 36 (1989), 1-21; Darrigol, op. cit., note 31.
132. 74 On Yukawa's work of 1933-38 see Laurie M. Brown, 'Yukawa's Prediction of the Meson', Centaurus 25 (1981), 71-132; Laurie M. Brown, 'How Yukawa Arrived at the Meson Theory', Progress of Theoretical Physics Supplement 85 (1985), 13-18; Laurie M. Brown, 'Yukawa in the 1930s: A Gentle Revolutionary', Historia Scientiarum 36 (1989), 1-21; Darrigol, op. cit., note 31.
133. 75 Yukawa translated Heisenberg's first two articles into Japanese with an introduction that was his first published paper; the text of this article is included in Brown, 'Prediction', op. cit., note 74.
134. 76 H. Yukawa, 'On the Interaction of Elementary Particles, I', Proceedings of the Physico-Mathematical Society of Japan 17 (1935). 48-57.
135. 77 Ibid., p. 48.
136. 78 More precisely, for the component of the 4-vector field corresponding to the electromagnetic scalar potential. Yukawa neglected the other three components on the assumption that the protons and neutrons were moving slowly.
137. 79 Op. cit., note 76, p. 51.
138. 80 H. Yukawa, 'A Comment on the Problem of Electrons in the Nucleus', in Kawabe, op. cit., note 15, p. 158. I am grateful to Dr Kawabe for photocopies of the manuscript and to Dr Kawabe and Dr Kubo of the Max-Planck-Institut, Munich, for discussions of this passage. A spelling error is corrected, and the rendering of the first sentence is slightly altered, for which change, however, Dr Kawabe is not to be held responsible. The words 'Platzwechsel der Ladung' appear in German in the text (cf. note 15); many other physics terms appear in English.
139. 81 Cf. Yukawa's manuscript 'The Roles of the Electron for Nuclear Structure' from roughly the same period, op. cit., note 15; as well as op. cit., note 76.
140. 81 Cf. Yukawa's manuscript 'The Roles of the Electron for Nuclear Structure' from roughly the same period, op. cit., note 15; as well as op. cit., note 76.
141. 82 In his memoirs Yukawa wrote of conceiving the electromagnetic interaction between charged particles as a game of 'catch', with the photon as the ball. It is not clear, however, how distinctly this was in his mind at the time. H. Yukawa, Tabibito (The Traveler), L. Brown and R. Yoshida (trans.) (Singapore: World Scientific, 1982), pp. 195-196.
142. 83 On the discovery of 'Yukawa's meson' see P. Galison, 'The Discovery of the Muon and the Failed Revolution Against Quantum Electrodynamics', Centaurus 26 (1983), 262-316; H. Rechenberg and L. M. Brown, 'Yukawa's Heavy Quantum and the Mesotron (1935-37)', Centaurus 33 (1990), 214-252; as well as D. C. Cassidy, 'Cosmic Ray Showers, High Energy Physics, and Quantum Field Theories: Programmatic Interactions in the 1930s', Historical Studies in the Physical and Biological Sciences 12(1) (1981), 1-39.
143. 83 On the discovery of 'Yukawa's meson' see P. Galison, 'The Discovery of the Muon and the Failed Revolution Against Quantum Electrodynamics', Centaurus 26 (1983), 262-316; H. Rechenberg and L. M. Brown, 'Yukawa's Heavy Quantum and the Mesotron (1935-37)', Centaurus 33 (1990), 214-252; as well as D. C. Cassidy, 'Cosmic Ray Showers, High Energy Physics, and Quantum Field Theories: Programmatic Interactions in the 1930s', Historical Studies in the Physical and Biological Sciences 12(1) (1981), 1-39.
144. 83 On the discovery of 'Yukawa's meson' see P. Galison, 'The Discovery of the Muon and the Failed Revolution Against Quantum Electrodynamics', Centaurus 26 (1983), 262-316; H. Rechenberg and L. M. Brown, 'Yukawa's Heavy Quantum and the Mesotron (1935-37)', Centaurus 33 (1990), 214-252; as well as D. C. Cassidy, 'Cosmic Ray Showers, High Energy Physics, and Quantum Field Theories: Programmatic Interactions in the 1930s', Historical Studies in the Physical and Biological Sciences 12(1) (1981), 1-39.
145. 84 That is not necessarily to say that Yukawa only thought in this way; he had done perturbation calculations of this sort on earlier versions of his theory, as laid out by Darrigol, op. cit., note 31, pp. 278-279. I am grateful to Olivier Darrigol for pointing this out to me.
146. 85 On various aspects of meson-field theories, see Visvapriya Mukherji, 'A History of the Meson Theory of Nuclear Forces from 1935 to 1952', Archive for History of Exact Sciences 13 (1974), 27-102; L. M. Brown and H. Rechenberg, 'Quantum Field Theories, Nuclear Forces, and the Cosmic Rays (1934-1938)', American Journal of Physics 59 (1991), 595-605; L. M. Brown and H. Rechenberg, 'The Development of the Vector Meson Theory in Britain and Japan (1937-38)', British Journal for History of Science 24 (1991), 405-433.
147. 85 On various aspects of meson-field theories, see Visvapriya Mukherji, 'A History of the Meson Theory of Nuclear Forces from 1935 to 1952', Archive for History of Exact Sciences 13 (1974), 27-102; L. M. Brown and H. Rechenberg, 'Quantum Field Theories, Nuclear Forces, and the Cosmic Rays (1934-1938)', American Journal of Physics 59 (1991), 595-605; L. M. Brown and H. Rechenberg, 'The Development of the Vector Meson Theory in Britain and Japan (1937-38)', British Journal for History of Science 24 (1991), 405-433.
148. 85 On various aspects of meson-field theories, see Visvapriya Mukherji, 'A History of the Meson Theory of Nuclear Forces from 1935 to 1952', Archive for History of Exact Sciences 13 (1974), 27-102; L. M. Brown and H. Rechenberg, 'Quantum Field Theories, Nuclear Forces, and the Cosmic Rays (1934-1938)', American Journal of Physics 59 (1991), 595-605; L. M. Brown and H. Rechenberg, 'The Development of the Vector Meson Theory in Britain and Japan (1937-38)', British Journal for History of Science 24 (1991), 405-433.
149. 86 e.g. G. C. Wick, 'Range of Forces in Yukawa's Theory', Nature 142 (1938), 993-994; G. Wentzel, 'Schwere Elektronen und Theorien der Kernvorgänge', Die Naturwissenschaften 26 (1938), 273-279.
150. 86 e.g. G. C. Wick, 'Range of Forces in Yukawa's Theory', Nature 142 (1938), 993-994; G. Wentzel, 'Schwere Elektronen und Theorien der Kernvorgänge', Die Naturwissenschaften 26 (1938), 273-279.
151. 87 H. Yukawa and S. Sakata, 'On the Interaction of Elementary Particles, II', Proceedings of the Physico-Mathematical Society of Japan, 19 (1937), 1084-1093; H. Yukawa, S. Sakata and M. Taketani, 'On the Interaction of Elementary Particles, III', Proceedings of the Physico-Mathematical Society of Japan 20 (1938), 319-340; N. Kemmer, 'Quantum Theory of Einstein-Bose Particles and Nuclear Interaction', Proceedings of the Royal Society of London A 166 (1938), 127-153; H. Fröhlich, W. Heitler, and N. Kemmer, 'On the Nuclear Forces and the Magnetic Moments of the Neutron and the Proton', Proceedings of the Royal Society of London A 166 (1938), 154-177; H. J. Bhabha, 'On the Theory of Heavy Electrons and Nuclear Forces', Proceedings of the Royal Society of London A 166 (1938), 501-528. The vector field also offered the hope, because of its spin, of a simple explanation of the proton and neutron magnetic moments.
152. 87 H. Yukawa and S. Sakata, 'On the Interaction of Elementary Particles, II', Proceedings of the Physico-Mathematical Society of Japan, 19 (1937), 1084-1093; H. Yukawa, S. Sakata and M. Taketani, 'On the Interaction of Elementary Particles, III', Proceedings of the Physico-Mathematical Society of Japan 20 (1938), 319-340; N. Kemmer, 'Quantum Theory of Einstein-Bose Particles and Nuclear Interaction', Proceedings of the Royal Society of London A 166 (1938), 127-153; H. Fröhlich, W. Heitler, and N. Kemmer, 'On the Nuclear Forces and the Magnetic Moments of the Neutron and the Proton', Proceedings of the Royal Society of London A 166 (1938), 154-177; H. J. Bhabha, 'On the Theory of Heavy Electrons and Nuclear Forces', Proceedings of the Royal Society of London A 166 (1938), 501-528. The vector field also offered the hope, because of its spin, of a simple explanation of the proton and neutron magnetic moments.
153. 87 H. Yukawa and S. Sakata, 'On the Interaction of Elementary Particles, II', Proceedings of the Physico-Mathematical Society of Japan, 19 (1937), 1084-1093; H. Yukawa, S. Sakata and M. Taketani, 'On the Interaction of Elementary Particles, III', Proceedings of the Physico-Mathematical Society of Japan 20 (1938), 319-340; N. Kemmer, 'Quantum Theory of Einstein-Bose Particles and Nuclear Interaction', Proceedings of the Royal Society of London A 166 (1938), 127-153; H. Fröhlich, W. Heitler, and N. Kemmer, 'On the Nuclear Forces and the Magnetic Moments of the Neutron and the Proton', Proceedings of the Royal Society of London A 166 (1938), 154-177; H. J. Bhabha, 'On the Theory of Heavy Electrons and Nuclear Forces', Proceedings of the Royal Society of London A 166 (1938), 501-528. The vector field also offered the hope, because of its spin, of a simple explanation of the proton and neutron magnetic moments.
154. 87 H. Yukawa and S. Sakata, 'On the Interaction of Elementary Particles, II', Proceedings of the Physico-Mathematical Society of Japan, 19 (1937), 1084-1093; H. Yukawa, S. Sakata and M. Taketani, 'On the Interaction of Elementary Particles, III', Proceedings of the Physico-Mathematical Society of Japan 20 (1938), 319-340; N. Kemmer, 'Quantum Theory of Einstein-Bose Particles and Nuclear Interaction', Proceedings of the Royal Society of London A 166 (1938), 127-153; H. Fröhlich, W. Heitler, and N. Kemmer, 'On the Nuclear Forces and the Magnetic Moments of the Neutron and the Proton', Proceedings of the Royal Society of London A 166 (1938), 154-177; H. J. Bhabha, 'On the Theory of Heavy Electrons and Nuclear Forces', Proceedings of the Royal Society of London A 166 (1938), 501-528. The vector field also offered the hope, because of its spin, of a simple explanation of the proton and neutron magnetic moments.
155. 87 H. Yukawa and S. Sakata, 'On the Interaction of Elementary Particles, II', Proceedings of the Physico-Mathematical Society of Japan, 19 (1937), 1084-1093; H. Yukawa, S. Sakata and M. Taketani, 'On the Interaction of Elementary Particles, III', Proceedings of the Physico-Mathematical Society of Japan 20 (1938), 319-340; N. Kemmer, 'Quantum Theory of Einstein-Bose Particles and Nuclear Interaction', Proceedings of the Royal Society of London A 166 (1938), 127-153; H. Fröhlich, W. Heitler, and N. Kemmer, 'On the Nuclear Forces and the Magnetic Moments of the Neutron and the Proton', Proceedings of the Royal Society of London A 166 (1938), 154-177; H. J. Bhabha, 'On the Theory of Heavy Electrons and Nuclear Forces', Proceedings of the Royal Society of London A 166 (1938), 501-528. The vector field also offered the hope, because of its spin, of a simple explanation of the proton and neutron magnetic moments.
156. 88 Because the meson, unlike the photon, had a non-zero mass, the longitudinal and time-like contributions to the Hamiltonian did not cancel as they did in QED. See, e.g. Fröhlich, Heitler, and Kemmer, op. cit., note 87, pp. 159-160, where the treatment parallels that in Heitler's book on QED (op. cit., note 46).
157. 89 This is not strictly true, as there was a term in the neutron-proton interaction that derived from the elimination of the fourth field component, which was not represented with field quanta, in the same way that the Coulomb interaction derived from the elimination of the non-transverse components in QED. This is, for instance, the last term in Yukawa, Sakata and Taketani, op. cit., note 87, p. 332, Eq. 47; cf. Kemmer, op. cit., note 87, p. 142, and Bhabha, op. cit., note 87, p. 518. The term represented a delta-function interaction of the neutron and proton. Because the charge change of the proton and neutron was written into the coupling, this term also effected an interchange of proton and neutron and could therefore be consolidated in the perturbative neutron-proton interaction with the terms arising from the absorption and emission of mesons.
158. 89 This is not strictly true, as there was a term in the neutron-proton interaction that derived from the elimination of the fourth field component, which was not represented with field quanta, in the same way that the Coulomb interaction derived from the elimination of the non-transverse components in QED. This is, for instance, the last term in Yukawa, Sakata and Taketani, op. cit., note 87, p. 332, Eq. 47; cf. Kemmer, op. cit., note 87, p. 142, and Bhabha, op. cit., note 87, p. 518. The term represented a delta-function interaction of the neutron and proton. Because the charge change of the proton and neutron was written into the coupling, this term also effected an interchange of proton and neutron and could therefore be consolidated in the perturbative neutron-proton interaction with the terms arising from the absorption and emission of mesons.
159. 90 For renormalization and its background see L. M. Brown (ed.), Renormalization: From Lorentz to Landau (and Beyond) (New York: Springer, 1993); Schweber, op. cit., note 45.
160. 90 For renormalization and its background see L. M. Brown (ed.), Renormalization: From Lorentz to Landau (and Beyond) (New York: Springer, 1993); Schweber, op. cit., note 45.
161. 91 Z. Koba, T. Tati and S. Tomonaga, 'On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields, III', Progress of Theoretical Physics 2 (1947), 198-208; S. Hayakawa, Y. Miyamoto and S. Tomonaga, 'On the Elimination of the Auxiliary Condition in the Quantum Electrodynamics, I', Journal of the Physical Society of Japan 2 (1947), 172-198; J. Schwinger, 'Quantum Electrodynamics, I, A Covariant Formulation', Physical Review 74 (1948), 1439-1461.
162. 91 Z. Koba, T. Tati and S. Tomonaga, 'On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields, III', Progress of Theoretical Physics 2 (1947), 198-208; S. Hayakawa, Y. Miyamoto and S. Tomonaga, 'On the Elimination of the Auxiliary Condition in the Quantum Electrodynamics, I', Journal of the Physical Society of Japan 2 (1947), 172-198; J. Schwinger, 'Quantum Electrodynamics, I, A Covariant Formulation', Physical Review 74 (1948), 1439-1461.
163. 91 Z. Koba, T. Tati and S. Tomonaga, 'On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields, III', Progress of Theoretical Physics 2 (1947), 198-208; S. Hayakawa, Y. Miyamoto and S. Tomonaga, 'On the Elimination of the Auxiliary Condition in the Quantum Electrodynamics, I', Journal of the Physical Society of Japan 2 (1947), 172-198; J. Schwinger, 'Quantum Electrodynamics, I, A Covariant Formulation', Physical Review 74 (1948), 1439-1461.
164. 92 J. Schwinger, 'Quantum Electrodynamics, II, Vacuum Polarization and Self-Energy', Physical Review 75 (1949), 651-679.
165. 93 See also S. S. Schweber, 'Feynman and the Visualization of Space Time Processes', Reviews of Modern Physics 58 (1986), 449-508.
166. 94 R. P. Feynman, 'The Development of the Space-Time View of Quantum Electrodynamics', Nobel lecture for 1965, in Nobel Lectures: Physics, 1963-1970 (Amsterdam: Elsevier, 1972), pp. 155-178, especially pp. 169-170, 172; cf. L. M. Brown, To Have Been a Student of Richard Feynman', in L. M. Brown and J. S. Rigden (eds). 'Most of the Good Stuff': Memories of Richard Feynman (New York: American Institute of Physics, 1993), pp. 53-58.
167. 94 R. P. Feynman, 'The Development of the Space-Time View of Quantum Electrodynamics', Nobel lecture for 1965, in Nobel Lectures: Physics, 1963-1970 (Amsterdam: Elsevier, 1972), pp. 155-178, especially pp. 169-170, 172; cf. L. M. Brown, To Have Been a Student of Richard Feynman', in L. M. Brown and J. S. Rigden (eds). 'Most of the Good Stuff': Memories of Richard Feynman (New York: American Institute of Physics, 1993), pp. 53-58.
168. 95 R. P. Feynman, 'Relativistic Cut-Off for Quantum Electrodynamics', Physical Review 74 (1948), 1430-1438.
169. 96 R. P. Feynman, 'Space-Time Approach to Quantum Electrodynamics', Physical Review 76 (1949), 769-789, see p. 772 and Section 8, 'Longitudinal Waves', pp. 780-781.
170. 97 S. T. Ma, 'Relativistic Formulation of the Quantum Theory of Radiation', Physical Review 75 (1949), 535; F. J. Belinfante, 'On the Part Played by Scalar and Longitudinal Photons in Ordinary Electromagnetic Fields', Physical Review 76 (1949), 226-233; N. Hu, 'On the Treatment of Quantum Electrodynamics Without Eliminating the Longitudinal Field', Physical Review 76 (1949), 391-396; F. J. Dyson, 'Longitudinal Photons in Quantum Electrodynamics', Physical Review 77 (1950), 420; F. Coester and J. M. Jauch, 'On the Role of the Subsidiary Condition in Quantum Electrodynamics', Physical Review 78 (1950), 149-157; S. N. Gupta, 'Theory of Longitudinal Photons in Quantum Electrodynamics', Proceedings of the Physical Society A 63 (1950), 681-691; K. Bleuler, 'Eine neue Methode zur Behandlung der longitudinalen und skalaren Photonen', Helvetica Physica Acta 23 (1950), 567-586.
171. 97 S. T. Ma, 'Relativistic Formulation of the Quantum Theory of Radiation', Physical Review 75 (1949), 535; F. J. Belinfante, 'On the Part Played by Scalar and Longitudinal Photons in Ordinary Electromagnetic Fields', Physical Review 76 (1949), 226-233; N. Hu, 'On the Treatment of Quantum Electrodynamics Without Eliminating the Longitudinal Field', Physical Review 76 (1949), 391-396; F. J. Dyson, 'Longitudinal Photons in Quantum Electrodynamics', Physical Review 77 (1950), 420; F. Coester and J. M. Jauch, 'On the Role of the Subsidiary Condition in Quantum Electrodynamics', Physical Review 78 (1950), 149-157; S. N. Gupta, 'Theory of Longitudinal Photons in Quantum Electrodynamics', Proceedings of the Physical Society A 63 (1950), 681-691; K. Bleuler, 'Eine neue Methode zur Behandlung der longitudinalen und skalaren Photonen', Helvetica Physica Acta 23 (1950), 567-586.
172. 97 S. T. Ma, 'Relativistic Formulation of the Quantum Theory of Radiation', Physical Review 75 (1949), 535; F. J. Belinfante, 'On the Part Played by Scalar and Longitudinal Photons in Ordinary Electromagnetic Fields', Physical Review 76 (1949), 226-233; N. Hu, 'On the Treatment of Quantum Electrodynamics Without Eliminating the Longitudinal Field', Physical Review 76 (1949), 391-396; F. J. Dyson, 'Longitudinal Photons in Quantum Electrodynamics', Physical Review 77 (1950), 420; F. Coester and J. M. Jauch, 'On the Role of the Subsidiary Condition in Quantum Electrodynamics', Physical Review 78 (1950), 149-157; S. N. Gupta, 'Theory of Longitudinal Photons in Quantum Electrodynamics', Proceedings of the Physical Society A 63 (1950), 681-691; K. Bleuler, 'Eine neue Methode zur Behandlung der longitudinalen und skalaren Photonen', Helvetica Physica Acta 23 (1950), 567-586.
173. 97 S. T. Ma, 'Relativistic Formulation of the Quantum Theory of Radiation', Physical Review 75 (1949), 535; F. J. Belinfante, 'On the Part Played by Scalar and Longitudinal Photons in Ordinary Electromagnetic Fields', Physical Review 76 (1949), 226-233; N. Hu, 'On the Treatment of Quantum Electrodynamics Without Eliminating the Longitudinal Field', Physical Review 76 (1949), 391-396; F. J. Dyson, 'Longitudinal Photons in Quantum Electrodynamics', Physical Review 77 (1950), 420; F. Coester and J. M. Jauch, 'On the Role of the Subsidiary Condition in Quantum Electrodynamics', Physical Review 78 (1950), 149-157; S. N. Gupta, 'Theory of Longitudinal Photons in Quantum Electrodynamics', Proceedings of the Physical Society A 63 (1950), 681-691; K. Bleuler, 'Eine neue Methode zur Behandlung der longitudinalen und skalaren Photonen', Helvetica Physica Acta 23 (1950), 567-586.
174. 97 S. T. Ma, 'Relativistic Formulation of the Quantum Theory of Radiation', Physical Review 75 (1949), 535; F. J. Belinfante, 'On the Part Played by Scalar and Longitudinal Photons in Ordinary Electromagnetic Fields', Physical Review 76 (1949), 226-233; N. Hu, 'On the Treatment of Quantum Electrodynamics Without Eliminating the Longitudinal Field', Physical Review 76 (1949), 391-396; F. J. Dyson, 'Longitudinal Photons in Quantum Electrodynamics', Physical Review 77 (1950), 420; F. Coester and J. M. Jauch, 'On the Role of the Subsidiary Condition in Quantum Electrodynamics', Physical Review 78 (1950), 149-157; S. N. Gupta, 'Theory of Longitudinal Photons in Quantum Electrodynamics', Proceedings of the Physical Society A 63 (1950), 681-691; K. Bleuler, 'Eine neue Methode zur Behandlung der longitudinalen und skalaren Photonen', Helvetica Physica Acta 23 (1950), 567-586.
175. 97 S. T. Ma, 'Relativistic Formulation of the Quantum Theory of Radiation', Physical Review 75 (1949), 535; F. J. Belinfante, 'On the Part Played by Scalar and Longitudinal Photons in Ordinary Electromagnetic Fields', Physical Review 76 (1949), 226-233; N. Hu, 'On the Treatment of Quantum Electrodynamics Without Eliminating the Longitudinal Field', Physical Review 76 (1949), 391-396; F. J. Dyson, 'Longitudinal Photons in Quantum Electrodynamics', Physical Review 77 (1950), 420; F. Coester and J. M. Jauch, 'On the Role of the Subsidiary Condition in Quantum Electrodynamics', Physical Review 78 (1950), 149-157; S. N. Gupta, 'Theory of Longitudinal Photons in Quantum Electrodynamics', Proceedings of the Physical Society A 63 (1950), 681-691; K. Bleuler, 'Eine neue Methode zur Behandlung der longitudinalen und skalaren Photonen', Helvetica Physica Acta 23 (1950), 567-586.
176. 97 S. T. Ma, 'Relativistic Formulation of the Quantum Theory of Radiation', Physical Review 75 (1949), 535; F. J. Belinfante, 'On the Part Played by Scalar and Longitudinal Photons in Ordinary Electromagnetic Fields', Physical Review 76 (1949), 226-233; N. Hu, 'On the Treatment of Quantum Electrodynamics Without Eliminating the Longitudinal Field', Physical Review 76 (1949), 391-396; F. J. Dyson, 'Longitudinal Photons in Quantum Electrodynamics', Physical Review 77 (1950), 420; F. Coester and J. M. Jauch, 'On the Role of the Subsidiary Condition in Quantum Electrodynamics', Physical Review 78 (1950), 149-157; S. N. Gupta, 'Theory of Longitudinal Photons in Quantum Electrodynamics', Proceedings of the Physical Society A 63 (1950), 681-691; K. Bleuler, 'Eine neue Methode zur Behandlung der longitudinalen und skalaren Photonen', Helvetica Physica Acta 23 (1950), 567-586.
177. 98 See, for example, F. J. Dyson, Advanced Quantum Mechanics, lecture notes for a course in relativistic quantum mechanics given at Cornell University in fall 1951, 2nd edn; W. Heitler, The Quantum Theory of Radiation, 3rd edn (Oxford: Oxford University Press, 1954); S. S. Schweber, II. A. Bethe and F. de Hoffman, Mesons and Fields, Vol. 1, Fields (Evanston, IL: Row and Peterson, 1955).
178. 98 See, for example, F. J. Dyson, Advanced Quantum Mechanics, lecture notes for a course in relativistic quantum mechanics given at Cornell University in fall 1951, 2nd edn; W. Heitler, The Quantum Theory of Radiation, 3rd edn (Oxford: Oxford University Press, 1954); S. S. Schweber, II. A. Bethe and F. de Hoffman, Mesons and Fields, Vol. 1, Fields (Evanston, IL: Row and Peterson, 1955).
179. 98 See, for example, F. J. Dyson, Advanced Quantum Mechanics, lecture notes for a course in relativistic quantum mechanics given at Cornell University in fall 1951, 2nd edn; W. Heitler, The Quantum Theory of Radiation, 3rd edn (Oxford: Oxford University Press, 1954); S. S. Schweber, II. A. Bethe and F. de Hoffman, Mesons and Fields, Vol. 1, Fields (Evanston, IL: Row and Peterson, 1955).
180. 99 See O. Darrigol. 'Elements of a Scientific Biography of Tomonaga Sin-itiro', Historia Scientiarum 35 (1988), 1-29; Schweber, op. cit., note 45, pp. 252-272.
181. 99 See O. Darrigol. 'Elements of a Scientific Biography of Tomonaga Sin-itiro', Historia Scientiarum 35 (1988), 1-29; Schweber, op. cit., note 45, pp. 252-272.