Bound states in quantum electrodynamics: Theory and application

Foundations of Physics

Volumn 32, Issue 9, 2002, Pages 1419-1457

  Grotch, H ^a   Owen, D A ^b  

^a UNIVERSITY OF KENTUCKY   (United States)

^b BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Bound states; Quantum electrodynamics

Indexed keywords

EID: 0036388124     PISSN: 00159018     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020311923535     Document Type: Article

References (57)

1. We draw freely from D. A. Owen, Proceedings of the Workshop on Quantum Infrared Physics, H. Fried and B. Müller, eds. (World Scientific, Singapore, 1995), pp. 244-261.
2. E. Salpeter, Phys. Rev. 87, 328 (1952).
3. Particle Properties Data Booklet (North-Holland, Amsterdam, 1988).
4. In theory, the energies of states which are not stable are branch points of the Green's function. However, perturbatively, they are seen as simple poles and the effects of their analytic properties are taken into account perturbatively. Formally, the homogeneous Bethe-Salpeter equation can be obtained in the usual way noting the product to two single particle dressed propagators have energy greater or equal to the sum of their masses which is unaffected by the existence of cuts. See also K. Nishijima, Phys. Rev. 111, 995 (1958) for a proof that stable states have simple poles.
5. G. Breit, Phys. Rev. 34, 553 (1929); 36, 383 (1930); 39 (1932).
6. G. Breit, Phys. Rev. 34, 553 (1929); 36, 383 (1930); 39 (1932).
7. G. Breit, Phys. Rev. 34, 553 (1929); 36, 383 (1930); 39 (1932).
8. W. Barker and F. Glover, Phys. Rev. 99, 317 (1955).
9. E. Salpeter and H. Bethe, Phys. Rev. 84, 1232 (1951), J. Schwinger, Proc. Natl. Acad. Sci. (U.S.A.) 37, 452 (1951). M. Gell-Mann and F. Low, Phys. Rev. 84, 350 (1951).
10. E. Salpeter and H. Bethe, Phys. Rev. 84, 1232 (1951), J. Schwinger, Proc. Natl. Acad. Sci. (U.S.A.) 37, 452 (1951). M. Gell-Mann and F. Low, Phys. Rev. 84, 350 (1951).
11. E. Salpeter and H. Bethe, Phys. Rev. 84, 1232 (1951), J. Schwinger, Proc. Natl. Acad. Sci. (U.S.A.) 37, 452 (1951). M. Gell-Mann and F. Low, Phys. Rev. 84, 350 (1951).
12. P. Roman, Introduction to Quantum Field Theory (Wiley, New York 1969).
13. -1," JHU thesis, 1970, unpublished.
14. R. Karplus and A. Klein, Phys. Rev. 87, 848 (1952). T. Fulton and P. Martin, Phys. Rev. 95, 811 (1954); for further details and references, see D. A. Owen, Topical Seminar on Electromagnetic Interactions (ICTP Trieste IC/71/140).
15. R. Karplus and A. Klein, Phys. Rev. 87, 848 (1952). T. Fulton and P. Martin, Phys. Rev. 95, 811 (1954); for further details and references, see D. A. Owen, Topical Seminar on Electromagnetic Interactions (ICTP Trieste IC/71/140).
16. R. Karplus and A. Klein, Phys. Rev. 87, 848 (1952). T. Fulton and P. Martin, Phys. Rev. 95, 811 (1954); for further details and references, see D. A. Owen, Topical Seminar on Electromagnetic Interactions (ICTP Trieste IC/71/140).
17. D. A. Owen, Phys. Rev. D 42, 2534 (1990). M. Halpert and D. A. Owen, J. Phys. G 20, 51 (1994). D. A. Owen, Found. Phys. 24, 273 (1994).
18. D. A. Owen, Phys. Rev. D 42, 2534 (1990). M. Halpert and D. A. Owen, J. Phys. G 20, 51 (1994). D. A. Owen, Found. Phys. 24, 273 (1994).
19. D. A. Owen, Phys. Rev. D 42, 2534 (1990). M. Halpert and D. A. Owen, J. Phys. G 20, 51 (1994). D. A. Owen, Found. Phys. 24, 273 (1994).
20. F. Gross, Phys. Rev. 186, 1448 (1969).
21. J. Gorelick and H. Grotch, J. Phys. G 3, 751 (1977).
22. G. Lepage, Phys. Rev. A 16, 863 (1977).
23. R. Blankenbecler and R. Sugar, Phys. Rev. 142, 1051 (1966).
24. F. Gross, Phys. Rev. 186, 1448 (1969).
25. A. Klein and B. Lee, Phys. Rev. D 10, 4308 (1974). A. Logunov and A. Tavkhelidze, Nuovo Cim. 29, 380 (1963).
26. A. Klein and B. Lee, Phys. Rev. D 10, 4308 (1974). A. Logunov and A. Tavkhelidze, Nuovo Cim. 29, 380 (1963).
27. H. Grotch and D. Yennie, Rev. Mod. Phys. 41, 350 (1969).
28. C. Fronsdal and R. Huff, Phys. Rev. D 3, 933 (1971).
29. H. Bethe and E. Salpeter, Phys. Rev. 84, 1232 (1951). J. Schwinger, Proc. Acad. Sci. 31, 452 (1951).
30. H. Bethe and E. Salpeter, Phys. Rev. 84, 1232 (1951). J. Schwinger, Proc. Acad. Sci. 31, 452 (1951).
31. -1.
32. Inadvertantly, undressed propagators are written. Here, we have corrected this oversight.
33. W. E. Caswell and G. P. Lepage, Phys. Lett. B 167, 437 (1986).
34. R. Blankenbecler and R. Sugar, Phys. Rev. 142, 1052 (1966).
35. In most of the general cases, we will consider both particles to be fermions as these are the most common systems that one encounters plus the possibility that all scalar particles, in fact, may be composite systems of fermions.
36. J. Bjorken and S. Drell, Relativistic Quantum Fields (McGraw-Hill, 1965) (cf. Chap. 19).
37. In this express and those that follow, we use matrix notation. Thus, in both the numerator and denominator, there are implied integrations.
38. G. Erickson and D. Yennie, Ann. Phys. (N.Y.) 35, 271, 447 (1965).
39. J. Fox and D. Yennie, Ann. Phys. (N.Y.) 81 (1973).
40. A. Logunov and A. Tavkhelidze, Nuovo Cim. 29, 380 (1963). A. Logunov et al., Nuovo Cim. 30, 134 (1963).
41. A. Logunov and A. Tavkhelidze, Nuovo Cim. 29, 380 (1963). A. Logunov et al., Nuovo Cim. 30, 134 (1963).
42. V. A. Rizov, Ann. Phys. 165, 59 (1985).
43. I. T. Todorov, Rep. Math. Phys. 24, 95 (1986).
44. V. A. Rizov, I. T. Todorov, and B. L. Aneva, Nucl. Phys. B 98, 447 (1975).
45. R. Duffin, Phys. Rev. 54, 1114 (1938). N. Kemmer, Proc. of Roy. Soc. (London) A 173, 91 (1939).
46. R. Duffin, Phys. Rev. 54, 1114 (1938). N. Kemmer, Proc. of Roy. Soc. (London) A 173, 91 (1939).
47. A. Akhiezer and V. Berestetskii, Quantum Electrodynamics (Interscience, 1965).
48. Y. Nedjadi and R. C. Barret, J. Phys. G 19, 87 (1993); preprint, University of Surrey "Solutions of the central field problem for a Duffin-Kemmer-Petiau vector boson."
49. Y. Nedjadi and R. C. Barret, J. Phys. G 19, 87 (1993); preprint, University of Surrey "Solutions of the central field problem for a Duffin-Kemmer-Petiau vector boson."
50. Chapter 9 of the reference given in footnote 35.
51. Private correspondence from R. Barrett.
52. I. Tamm, J. Phys. (U.S.S.R.) 9, 449 (1945). S. M. Dancoff, Phys. Rev. 78, 382 (1950).
53. I. Tamm, J. Phys. (U.S.S.R.) 9, 449 (1945). S. M. Dancoff, Phys. Rev. 78, 382 (1950).
54. H. Bethe and E. Salpeter, Quantum Mechanics of One- and Two-Electron Systems (Springer, Berlin 1957).
55. Private communication, M. Eides.
56. The form of this transformation is found in most field theory books, for example, J. Bjorken and S. Drell, Relativistic Quantum Fields (McGraw-Hill, 1965).
57. V. Rizov and I. Todorov, Sov. J. Part. Nucl. 6, 269 (1976).