A relativistic Schrödinger-like equation for a photon and its second quantization

Foundations of Physics

Volumn 29, Issue 8, 1999, Pages 1203-1231

  Kobe, Donald H ^a  

^a UNIVERSITY OF NORTH TEXAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033262665     PISSN: 00159018     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1018855630724     Document Type: Article

References (56)

1. M. O. Scully and M. S. Zubairy. Quantum Optics (Cambridge University Press, Cambridge, 1997), pp. 24-45.
2. C. Lanczos, Z. Phys. 57, 447-473 (1929).
3. G. Rumer, Z. Phys. 65, 244-252 (1930).
4. O. Laporte and G. E. Uhlenbeck, Phys. Rev. 37, 1380-1397 (1931).
5. G. Molière. Ann. Phys. (Leipzig) 37, 415-420 (1940).
6. G. Molière. Ann. Phys. (Leipzig) 6, 146-162 (1949).
7. J. R. Oppenheimer, Phys. Rev. 38, 725-746 (1931).
8. W. J. Archibald, Can. J. Phys. 33, 565-572 (1955).
9. R. H. Good, Jr., Phys. Rev. 105, 1914-1919 (1957).
10. C. L. Hammer and R. H. Good, Jr., Phys. Rev. 108, 882-886 (1957).
11. T. J. Nelson and R. H. Good, Jr., Phys. Rev. 179, 1445-1449 (1969).
12. R. H. Good, Jr., and T. J. Nelson, Classical Theory of Electric and Magnetic Fields (Academic, New York, 1971), pp. 578-627.
13. J. J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley, Reading, MA, 1967), pp. 23-32, 169 (note).
14. J. E. Sipe, Phys. Rev. A 52, 1875-1883 (1995).
15. I. Bialynicki-Birula, Acta Phys. Polonica A 86, 97-116 (1994).
16. B. Kursunoǧlu, Modern Quantum Theory (Freeman, San Francisco, 1962), Chap. II.
17. I. Białynicki-Birula, in Progress in Optics, Vol. XXXVI, E. Wolf, ed. (North-Holland, Amsterdam, 1996), pp. 245-294.
18. A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics (Interscience, New York, 1965), pp. 1-72.
19. R. A. Young, Am. J. Phys. 44, 1043-1046 (1976).
20. E. C. G. Sudarshan and T. Rothman. Am. J. Phys. 59, 592-595 (1991).
21. E. Merzbacher and D. Park, Am. J. Phys. 60, 946 (1992).
22. A. H. Godlevskaya and V. N. Kapshai, Opt. Spektrosk. 66, 830-834 (1989). [English translation: Opt. Spectrosc. (USSR) 66, 486-488 (1989).]
23. A. H. Godlevskaya and V. N. Kapshai, Opt. Spektrosk. 66, 830-834 (1989). [English translation: Opt. Spectrosc. (USSR) 66, 486-488 (1989).]
24. I. K. Karpenko, Izvest. Vysshikh Uchebnykh Zavedenii Fiz. 32, 46-50 (1989). [English translation: Soviet Phys. J. 32, 708-712 (1989).]
25. I. K. Karpenko, Izvest. Vysshikh Uchebnykh Zavedenii Fiz. 32, 46-50 (1989). [English translation: Soviet Phys. J. 32, 708-712 (1989).]
26. W. I. Fushchich and A. G. Nikitin, Symmetries of Maxwell's Equations (Reidel, Dordrecht, 1987), pp. 8-20.
27. R. J. Cook, Phys. Rev. A 25, 2164-2167 (1982).
28. R. J. Cook, Phys. Rev. A 26, 2754-2760 (1982).
29. R. Mignani, E. Recami, and M. Baldo, Lett. Nuovo Cimento 11, 568-572 (1974).
30. R. P. Feynman, Quantum Electrodynamics (Benjamin, New York, 1962), pp. 66-70.
31. R. P. Feynman, Phys. Rev. 76, 749-759 (1949).
32. K. Gottfried, Quantum Mechanics, Vol. I: Fundamentals (Benjamin, New York, 1966). pp. 400-418. (Circular polarization vectors are given on p. 413.)
33. H. Weber, Die partiellen Differential-Gleichungen der mathematischen Physik nach Riemann's Vorlesungen (Vieweg, Braunschweig, 1901), p. 348.
34. H. Kramers, Quantum Mechanics (North-Holland, Amsterdam, 1958), pp. 418-422. [Reprinted: (Dover, New York, 1964.)] [Kramers does not use λ in his definition of F̄ in Eq. (2.5).]
35. L. Silberstein. Phil. Mag. 23, 790-809 (1912).
36. H. Bateman, The Mathematical Analysis of Electrical and Optical Wavemotion on the Basis of Maxwell's Equations (Cambridge University Press, Cambridge, 1915), pp. 4, 5. [Reprinted: (Dover, New York, 1955).]
37. J. D. Jackson, Classical Electrodynamics, 2nd edn. (Wiley, New York, 1975), pp. 236-237, 245-251.
38. D. Bohm, Quantum Theory (Prentice Hall, Englewood Cliffs, NJ, 1951), pp. 89-98. 108-110. [Reprinted: (Dover, New York, 1989).]
39. T. D. Newton and E. P. Wigner, Rev. Mod. Phys. 21, 400-406 (1949).
40. A. S. Wightman, Rev. Mod. Phys. 34, 845-872 (1962).
41. J. M. Jauch and C. Piron, Helv. Phys. Acta 40, 559-570 (1967).
42. W. O. Amrein, Helv. Phys. Acta 42, 149-190 (1968).
43. I. Białynicki-Birula, Phys. Rev. Lett. 80, 5247-5250 (1998).
44. L. D. Landau and R. Peierls, Z. Phys. 62, 188-200 (1930).
45. L. Mandel, Phys. Rev. 144, 1071-1077 (1966).
46. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, New York, 1995), pp. 629-639.
47. G. Baym, Lectures on Quantum Mechanics (Benjamin, New York, 1969), Chap. 1.
48. W. Pauli and V. Weisskopf, Helv. Phys. Acta 7, 709-731 (1934).
49. S. J. van Enk and G. Nienhuis, Europhys. Lett. 25, 497-501 (1994).
50. D. H. Kobe, Phys. Lett. A 253, 7-11 (1999).
51. D. H. Kobe, Am. J. Phys. 49, 581-588 (1981).
52. W. Heitler, The Quantum Theory of Radiation, 3rd edn. (Oxford University Press, London, 1954), Chap. II.
53. D. H. Kobe and R. D. Gray, J. Phys. A Math. Gen. 15, 3145-3155 (1982).
54. R. Loudon, The Quantum Theory of Light (Oxford University Press, London, 1973), Chap. 6.
55. J. Schwinger, Phys. Rev. 127, 324-330 (1962).
56. S. Weinberg, The Quantum Theory of Fields, Vol. 1. Foundations (Cambridge University Press, Cambridge, 1995), p. 375.