Sphalerons, spectral flow, and anomalies

Journal of Mathematical Physics

Volumn 44, Issue 8, 2003, Pages 3619-3639

  Klinkhamer, Frans R ^a   Rupp, Christian ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042229071     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1590420     Document Type: Review

References (86)

1. H. R. Skyrme, Proc. R. Soc. London, Ser. A 260, 127 (1960); Nucl. Phys. 31, 556 (1962).
2. H. R. Skyrme, Proc. R. Soc. London, Ser. A 260, 127 (1960); Nucl. Phys. 31, 556 (1962).
3. G. 't Hooft, Nucl. Phys. B 79, 276 (1974); A. M. Polyakov, JETP Lett. 20,194 (1974) [Pisma Zh. Eksp. Teor. Fiz. 20 430 (1974)].
4. G. 't Hooft, Nucl. Phys. B 79, 276 (1974); A. M. Polyakov, JETP Lett. 20,194 (1974) [Pisma Zh. Eksp. Teor. Fiz. 20 430 (1974)].
5. G. 't Hooft, Nucl. Phys. B 79, 276 (1974); A. M. Polyakov, JETP Lett. 20,194 (1974) [Pisma Zh. Eksp. Teor. Fiz. 20 430 (1974)].
6. C. H. Taubes, Commun. Math. Phys. 86, 257 (1982); 86, 299 (1982); 97, 473 (1985).
7. C. H. Taubes, Commun. Math. Phys. 86, 257 (1982); 86, 299 (1982); 97, 473 (1985).
8. C. H. Taubes, Commun. Math. Phys. 86, 257 (1982); 86, 299 (1982); 97, 473 (1985).
9. N. S. Manton, Phys. Rev. D 28, 2019 (1983).
10. F. R. Klinkhamer and N. S. Manton, Phys. Rev. D 30, 2212 (1984).
11. F. R. Klinkhamer, Nucl. Phys. B 410, 343 (1993).
12. F. R. Klinkhamer and P. Olesen, Nucl. Phys. B 422, 227 (1994).
13. S. L. Glashow, Nucl. Phys. 22, 579 (1961); S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967); A. Salam, "Weak and electromagnetic interactions," in Elementary Particle Theory, edited by N. Svartholm (Almqvist, Stockholm, 1968), p. 367; S. L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D 2, 1285 (1970).
14. S. L. Glashow, Nucl. Phys. 22, 579 (1961); S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967); A. Salam, "Weak and electromagnetic interactions," in Elementary Particle Theory, edited by N. Svartholm (Almqvist, Stockholm, 1968), p. 367; S. L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D 2, 1285 (1970).
15. S. L. Glashow, Nucl. Phys. 22, 579 (1961); S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967); A. Salam, "Weak and electromagnetic interactions," in Elementary Particle Theory, edited by N. Svartholm (Almqvist, Stockholm, 1968), p. 367; S. L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D 2, 1285 (1970).
16. S. L. Glashow, Nucl. Phys. 22, 579 (1961); S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967); A. Salam, "Weak and electromagnetic interactions," in Elementary Particle Theory, edited by N. Svartholm (Almqvist, Stockholm, 1968), p. 367; S. L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D 2, 1285 (1970).
17. L. D. McLerran, Acta Phys. Pol. B 25, 309 (1994).
18. V. A. Rubakov and M. E. Shaposhnikov, Usp. Fiz. Nauk 166 493 (1996) [Phys. Usp. 39, 461 (1996)].
19. V. A. Rubakov and M. E. Shaposhnikov, Usp. Fiz. Nauk 166 493 (1996) [Phys. Usp. 39, 461 (1996)].
20. M. Nakahara, Geometry, Topology and Physics (Institute of Physics Publishing, Bristol, 1990).
21. J. Milnor, Morse Theory (Princeton University Press, Princeton, 1963).
22. R. Dashen, B. Hasslacher, and A. Neveu, Phys. Rev. D 10, 4138 (1974).
23. F. R. Klinkhamer, Phys. Lett. B 236, 187 (1990).
24. J. Kunz, B. Kleihaus, and Y. Brihaye, Phys. Rev. D 46, 3587 (1992).
25. M. Hindmarsh and M. James, Phys. Rev. D 49, 6109 (1994).
26. J. Kunz and Y. Brihaye, Phys. Lett. B 216, 353 (1989).
27. L. G. Yaffe, Phys. Rev. D 40, 3463 (1989).
28. F. R. Klinkhamer, Z. Phys. C 29, 153 (1985).
29. F. Wilczek and A. Zee, Phys. Rev. Lett. 51, 2250 (1983).
30. R. S. Palais, Commun. Math. Phys. 69, 19 (1979).
31. H. B. Nielsen and P. Olesen, Nucl. Phys. B 61, 45 (1973).
32. Y. Nambu, Nucl. Phys. B 130, 505 (1977).
33. M. James, L. Perivolaropoulos, and T. Vachaspati, Nucl. Phys. B 395, 534 (1993).
34. S. L. Adler, Phys. Rev. 177, 2426 (1969).
35. J. S. Bell and R. Jackiw, Nuovo Cimento A 60, 47 (1969).
36. S. L. Adler and W. A. Bardeen, Phys. Rev. 182, 1517 (1969).
37. W. A. Bardeen, Phys. Rev. 184, 1848 (1969).
38. C. Bouchiat, J. Iliopoulos, and P. Meyer, Phys. Lett. 38B, 519 (1972).
39. D. J. Gross and R. Jackiw, Phys. Rev. D 6, 477 (1972).
40. E. Witten, Phys. Lett. 117B, 324 (1982).
41. M. Atiyah, V. K. Patodi, and I. M. Singer, Math. Proc. Cambridge Philos. Soc. 77, 43 (1975); 78, 405 (1975); 79, 71 (1976).
42. M. Atiyah, V. K. Patodi, and I. M. Singer, Math. Proc. Cambridge Philos. Soc. 77, 43 (1975); 78, 405 (1975); 79, 71 (1976).
43. M. Atiyah, V. K. Patodi, and I. M. Singer, Math. Proc. Cambridge Philos. Soc. 77, 43 (1975); 78, 405 (1975); 79, 71 (1976).
44. M. Atiyah, "Topological aspects of anomalies," in Symposium on Anomalies, Geometry, Topology, edited by W. A. Bardeen and A. R. White (World Scientific, Singapore, 1985), p. 22.
45. C. R. Nohl, Phys. Rev. D 12, 1840 (1975).
46. R. Jackiw and C. Rebbi, Phys. Rev. D 13, 3398 (1976).
47. F. R. Klinkhamer and N. S. Manton, "A saddle-point solution in the Weinberg-Salam theory," in Proceedings of the 1984 Summer Study on the Design and Utilization of the Superconducting Super Collider, edited by R. Donaldson and J. Morfin (American Physical Society, New York, 1984), p. 805.
48. A. Ringwald, Phys. Lett. B 213, 61 (1988).
49. J. Kunz and Y. Brihaye, Phys. Lett. B 304, 141 (1993).
50. M. Atiyah and I. M. Singer, Ann. Math. 87, 484 (1968); 87, 546 (1968); 93, 119 (1971).
51. M. Atiyah and I. M. Singer, Ann. Math. 87, 484 (1968); 87, 546 (1968); 93, 119 (1971).
52. M. Atiyah and I. M. Singer, Ann. Math. 87, 484 (1968); 87, 546 (1968); 93, 119 (1971).
53. A. A. Belavin, A. M. Polyakov, A. S. Schwartz, and Y. S. Tyupkin, Phys. Lett. 59B, 85 (1975).
54. K. M. Bitar and S. J. Chang, Phys. Rev. D 17, 486 (1978).
55. F. R. Klinkhamer, Nucl. Phys. B 407, 88 (1993).
56. F. R. Klinkhamer and J. Weller, Nucl. Phys. B 481, 403 (1996).
57. F. R. Klinkhamer, Nucl. Phys. B 517, 142 (1998).
58. O. Bär, Nucl. Phys. B 650, 522 (2003).
59. F. R. Klinkhamer and C. Rupp, Nucl. Phys. B 495, 172 (1997).
60. R. Jackiw and P. Rossi, Nucl. Phys. B 190, 681 (1981).
61. M. A. Earnshaw and W. B. Perkins, Phys. Lett. B 328, 337 (1994).
62. N. S. Manton, Ann. Phys. (N.Y.) 159, 220 (1985).
63. R. Jackiw and C. Rebbi, Phys. Rev. D 16, 1052 (1977).
64. K. Fujikawa, Phys. Rev. D 21, 2848 (1980); erratum, 22, 1499 (1980).
65. R. A. Bertlmann, Anomalies in Quantum Field Theory (Oxford University Press, Oxford, 2000).
66. G. 't Hooft, Phys. Rev. Lett. 37, 8 (1976).
67. G. 't Hooft, Phys. Rev. D 14, 3432 (1976); erratum, 18, 2199 (1978).
68. N. H. Christ, Phys. Rev. D 21, 1591 (1980).
69. T. M. Gould and S. D. Hsu, Nucl. Phys. B 446, 35 (1995).
70. V. V. Khoze, Nucl. Phys. B 445, 270 (1995).
71. S. Dimopoulos and L. Susskind, Phys. Rev. D 18, 4500 (1978).
72. A. Ringwald, Nucl. Phys. B 330, 1 (1990); O. Espinosa, ibid. 343, 310 (1990); S. Y. Khlebnikov, V. A. Rubakov, and P. G. Tinyakov, ibid. 350, 441 (1991).
73. A. Ringwald, Nucl. Phys. B 330, 1 (1990); O. Espinosa, ibid. 343, 310 (1990); S. Y. Khlebnikov, V. A. Rubakov, and P. G. Tinyakov, ibid. 350, 441 (1991).
74. A. Ringwald, Nucl. Phys. B 330, 1 (1990); O. Espinosa, ibid. 343, 310 (1990); S. Y. Khlebnikov, V. A. Rubakov, and P. G. Tinyakov, ibid. 350, 441 (1991).
75. E. Farhi, V. V. Khoze, and R. Singleton, Phys. Rev. D 47, 5551 (1993).
76. F. R. Klinkhamer and Y. J. Lee, Phys. Rev. D 64, 065024 (2001).
77. F. R. Klinkhamer, "Electroweak baryon number violation," in XIV-th Rencontre de Blois: Matter-Antimatter Asymmetry, edited by L. Iconomidou-Fayard and J. Tran Thanh Van, in press [hep-ph/0209227].
78. M. F. Atiyah and I. M. Singer, Ann. Math. 93, 139 (1971).
79. S. Elitzur and V. P. Nair, Nucl. Phys. B 243, 205 (1984).
80. F. R. Klinkhamer, Phys. Lett. B 256, 41 (1991).
81. M. V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984).
82. P. Nelson and L. Alvarez-Gaumé, Commun. Math. Phys. 99, 103 (1985).
83. F. R. Klinkhamer, Nucl. Phys. B 535, 233 (1998).
84. F. R. Klinkhamer, Nucl. Phys. B 578, 277 (2000).
85. F. R. Klinkhamer and J. Schimmel, Nucl. Phys. B 639, 241 (2002).
86. F. R. Klinkhamer, "CPT violation: mechanism and phenomenology, " in Proceedings of the Seventh International Wigner Symposium, edited by M. E. Noz, in press [hep-th/0110135].