On the equivalence between sine-Gordon model and thirring model in the chirally broken phase of the Thirring model

European Physical Journal C

Volumn 20, Issue 4, 2001, Pages 723-757

  Faber, M ^b   Ivanov, A N ^a,b  

^a PETER THE GREAT ST PETERSBURG POLYTECHNIC UNIVERSITY   (Russian Federation)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001212310     PISSN: 14346044     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100520100694     Document Type: Article

References (71)

1. M. Remoissenet, in Waves called solitons, concepts and experiments (Springer-Verlag, Heidelberg 1994)
2. W. Thirring, Ann. Phys. (N.Y.) 3, 91 (1958)
3. S. Coleman, Phys. Rev. D 11, 2088 (1975)
4. T.H.R. Skyrme, Proc. Roy. Soc. A 247, 260 (1958); ibid. A 262, 237 (1961)
5. T.H.R. Skyrme, Proc. Roy. Soc. A 247, 260 (1958); ibid. A 262, 237 (1961)
6. B. Klaiber, in Lectures in theoretical physics, Lectures delivered at the Summer Institute for Theoretical Physics, University of Colorado, Boulder, 1967, edited by A. Barut, W. Brittin (Gordon and Breach, New York 1968), Vol. X, part A, pp. 141-176
7. K. Furuya, Re.E. Gamboa Saravi, F.A. Schaposnik, Nucl. Phys. B 208, 159 (1982)
8. J. Fröhlich, P. Marchetti, Commun. Math. Phys. 116, 127 (1988)
9. S. Mandelstam, Phys. Rev. D 11, 3026 (1975)
10. P.H. Damgaard, H.B. Nielsen, R. Sollacher, Nucl. Phys. B 385, 227 (1992) and references therein
11. J. Thomassen, PhD, TUWien, 15 January 2000
12. J. Alfaro, P.H. Damgaard, Ann. of Phys. (N.Y.) 202, 398 (1990)
13. K. Fujikawa, Phys. Rev. Lett. 44, 1195 (1979); Phys. Rev. D 21, 2848 (1982); Phys. Rev. D 22, 1499(E) (1980)
14. K. Fujikawa, Phys. Rev. Lett. 44, 1195 (1979); Phys. Rev. D 21, 2848 (1982); Phys. Rev. D 22, 1499(E) (1980)
15. K. Fujikawa, Phys. Rev. Lett. 44, 1195 (1979); Phys. Rev. D 21, 2848 (1982); Phys. Rev. D 22, 1499(E) (1980)
16. R. Roskies, F.A. Schaposnik, Phys. Rev. D 23, 558 (1981); R.E. Gamboa Saravi, F.A. Schaposnik, J.E. Solomin, Nucl. Phys. B 153, 112 (1979); R.E. Gamboa Savari, M.A. Muschetti, F.A. Schaposnik, J. E. Solomin, Ann. of Phys. (N.Y.) 157, 360 (1984)
17. R. Roskies, F.A. Schaposnik, Phys. Rev. D 23, 558 (1981); R.E. Gamboa Saravi, F.A. Schaposnik, J.E. Solomin, Nucl. Phys. B 153, 112 (1979); R.E. Gamboa Savari, M.A. Muschetti, F.A. Schaposnik, J. E. Solomin, Ann. of Phys. (N.Y.) 157, 360 (1984)
18. R. Roskies, F.A. Schaposnik, Phys. Rev. D 23, 558 (1981); R.E. Gamboa Saravi, F.A. Schaposnik, J.E. Solomin, Nucl. Phys. B 153, 112 (1979); R.E. Gamboa Savari, M.A. Muschetti, F.A. Schaposnik, J. E. Solomin, Ann. of Phys. (N.Y.) 157, 360 (1984)
19. O. Alvarez, Nucl. Phys. B 238, 61 (1984)
20. S.K. Hu, B.L. Young, D.W. McKay, Phys. Rev. D 30, 836 (1984), C.M. Naón, Phys. Rev. D 31, 2035 (1985)
21. S.K. Hu, B.L. Young, D.W. McKay, Phys. Rev. D 30, 836 (1984), C.M. Naón, Phys. Rev. D 31, 2035 (1985)
22. H. Dorn, Phys. Lett. B 167, 86 (1986)
23. R.A. Bertlmann, in Anomalies in quantum field theory, Oxford Science Publications (Clarendon Press, Oxford 1996), pp. 248-286
24. Y. Nambu, G. Jona-Lasinio, Phys. Rev. 122, 345 (1961); ibid. 124, 246 (1961)
25. Y. Nambu, G. Jona-Lasinio, Phys. Rev. 122, 345 (1961); ibid. 124, 246 (1961)
26. K. Kikkawa, Progr. Theor. Phys. 56, 947 (1976); H. Kleinert, Proceedings of International Summer School of Subnuclear Physics, Erice 1976, edited by A. Zichichi, p. 289; A. Dhar, R. Shankar, S.R. Wadia, Phys. Rev. D 31, 3256 (1985); D. Ebert, H. Reinhardt, Nucl. Phys. B 271, 188 (1986); M. Wakamatsu, Ann. of Phys. (N.Y.) 193, 287 (1989)
27. K. Kikkawa, Progr. Theor. Phys. 56, 947 (1976); H. Kleinert, Proceedings of International Summer School of Subnuclear Physics, Erice 1976, edited by A. Zichichi, p. 289; A. Dhar, R. Shankar, S.R. Wadia, Phys. Rev. D 31, 3256 (1985); D. Ebert, H. Reinhardt, Nucl. Phys. B 271, 188 (1986); M. Wakamatsu, Ann. of Phys. (N.Y.) 193, 287 (1989)
28. K. Kikkawa, Progr. Theor. Phys. 56, 947 (1976); H. Kleinert, Proceedings of International Summer School of Subnuclear Physics, Erice 1976, edited by A. Zichichi, p. 289; A. Dhar, R. Shankar, S.R. Wadia, Phys. Rev. D 31, 3256 (1985); D. Ebert, H. Reinhardt, Nucl. Phys. B 271, 188 (1986); M. Wakamatsu, Ann. of Phys. (N.Y.) 193, 287 (1989)
29. K. Kikkawa, Progr. Theor. Phys. 56, 947 (1976); H. Kleinert, Proceedings of International Summer School of Subnuclear Physics, Erice 1976, edited by A. Zichichi, p. 289; A. Dhar, R. Shankar, S.R. Wadia, Phys. Rev. D 31, 3256 (1985); D. Ebert, H. Reinhardt, Nucl. Phys. B 271, 188 (1986); M. Wakamatsu, Ann. of Phys. (N.Y.) 193, 287 (1989)
30. K. Kikkawa, Progr. Theor. Phys. 56, 947 (1976); H. Kleinert, Proceedings of International Summer School of Subnuclear Physics, Erice 1976, edited by A. Zichichi, p. 289; A. Dhar, R. Shankar, S.R. Wadia, Phys. Rev. D 31, 3256 (1985); D. Ebert, H. Reinhardt, Nucl. Phys. B 271, 188 (1986); M. Wakamatsu, Ann. of Phys. (N.Y.) 193, 287 (1989)
31. S.P. Klevansky, Rev. Mod. Phys. 64, 649 (1992); T. Hatsuda, T. Kunihiro, Phys. Rep. 247, 221 (1994)
32. S.P. Klevansky, Rev. Mod. Phys. 64, 649 (1992); T. Hatsuda, T. Kunihiro, Phys. Rep. 247, 221 (1994)
33. A.N. Ivanov, M. Nagy, N.I. Troitskaya, Int. J. Mod. Phys. A 7, 7305 (1992); A.N. Ivanov, Int. J. Mod. Phys. A 8, 853 (1993)
34. A.N. Ivanov, M. Nagy, N.I. Troitskaya, Int. J. Mod. Phys. A 7, 7305 (1992); A.N. Ivanov, Int. J. Mod. Phys. A 8, 853 (1993)
35. M. Faber, A.N. Ivanov, W. Kainz, N.I. Troitskaya, Z. Phys. C 74, 721 (1997); Phys. Lett. B 386, 198 (1996); M. Faber, A.N. Ivanov, A. Müller, N.I. Troitskaya, M. Zach, Eur. Phys. J. C 7, 685 (1999); ibid. C 10, 537 (1999)
36. M. Faber, A.N. Ivanov, W. Kainz, N.I. Troitskaya, Z. Phys. C 74, 721 (1997); Phys. Lett. B 386, 198 (1996); M. Faber, A.N. Ivanov, A. Müller, N.I. Troitskaya, M. Zach, Eur. Phys. J. C 7, 685 (1999); ibid. C 10, 537 (1999)
37. M. Faber, A.N. Ivanov, W. Kainz, N.I. Troitskaya, Z. Phys. C 74, 721 (1997); Phys. Lett. B 386, 198 (1996); M. Faber, A.N. Ivanov, A. Müller, N.I. Troitskaya, M. Zach, Eur. Phys. J. C 7, 685 (1999); ibid. C 10, 537 (1999)
38. M. Faber, A.N. Ivanov, W. Kainz, N.I. Troitskaya, Z. Phys. C 74, 721 (1997); Phys. Lett. B 386, 198 (1996); M. Faber, A.N. Ivanov, A. Müller, N.I. Troitskaya, M. Zach, Eur. Phys. J. C 7, 685 (1999); ibid. C 10, 537 (1999)
39. J. Bardeen, L.N. Cooper, J.R. Schrieffer, Phys. Rev. 106, 162 (1957); Phys. Rev. 108, 1175 (1957)
40. J. Bardeen, L.N. Cooper, J.R. Schrieffer, Phys. Rev. 106, 162 (1957); Phys. Rev. 108, 1175 (1957)
41. A.N. Ivanov, Nonperturbative phenomena in quantum chromodynamics, Lectures delivered at Institute of Nuclear Physics in Vienna University of Technology in Winter semester in 1995, Part 2
42. N.D. Mermin, H. Wagner, Phys. Rev. Lett. 17, 1133 (1966)
43. S. Coleman, Comm. Math. Phys. 31, 259 (1973)
44. C. Itzykson, J.-B. Zuber, in Quantum field theory (McGraw-Hill Book Company, New York 1980), p. 525
45. K. Huang, in Quantum field theory, From operators to path integrals (John Wiley and Sons, Inc., New York 1998), pp. 363-367
46. E.M. Lifshitz, L.P. Pitaevskii, in Relativistic quantum theory, part 2 (Pergamon Press, New York 1974), p. 503; (see also [17], p. 136)
47. C.G. Callan, R.F. Dashen, D.H. Sharp, Phys. Rev. 165, 1883 (1968)
48. H. Sugawara, Phys. Rev. 170, 1659 (1968)
49. C.M. Sommerfield, Phys. Rev. 176, 2019 (1968); H. Georgi, Phys. Rev. D 2, 2908 (1970)
50. C.M. Sommerfield, Phys. Rev. 176, 2019 (1968); H. Georgi, Phys. Rev. D 2, 2908 (1970)
51. J. Schwinger, Phys. Rev. Lett. 3, 296 (1959)
52. C.M. Sommerfield, Ann. of Phys. (N.Y.) 26, 1 (1963)
53. D. Finkelstein, J. Math. Phys. 7, 1218 (1966); L.D. Faddeev, V.E. Korepin, Phys. Rep. C 42, 1 (1978) (see also [28], pp. 380-388)
54. D. Finkelstein, J. Math. Phys. 7, 1218 (1966); L.D. Faddeev, V.E. Korepin, Phys. Rep. C 42, 1 (1978) (see also [28], pp. 380-388)
55. M. Gell-Mann, R.J. Oakes, B. Renner, Phys. Rev. 175, 2195 (1968)
56. P.C. Hohenberg, Phys. Rev. 158, 383 (1967)
57. P.B. Vigman, A.I. Larkin, Zh. Exper. Theor. Fiz. 72, 857 (1977) (in Russian)
58. J. Goldstone, Nuovo Cimento 19, 154 (1961); J. Goldstone, A. Salam, S. Weinberg, Phys. Rev. 127, 965 (1962)
59. J. Goldstone, Nuovo Cimento 19, 154 (1961); J. Goldstone, A. Salam, S. Weinberg, Phys. Rev. 127, 965 (1962)
60. See [27], pp. 519-521
61. T. Appelquist, J. Carazzone, Phys. D 11, 2856 (1975)
62. M. Faber, Few Body System 30, 149 (2001)
63. K. Göke, J.N. Urbano, M. Fiolhais, M. Harvey, Phys. Lett. B 164, 249 (1985)
64. See [17], pp. 284-286
65. D.J. Gross, R. Jackiw, Phys. Rev. D 6, 477 (1972); L. Dolan, R. Jackiw, Phys. Rev. D 9, 2904 (1974)
66. D.J. Gross, R. Jackiw, Phys. Rev. D 6, 477 (1972); L. Dolan, R. Jackiw, Phys. Rev. D 9, 2904 (1974)
67. A. Salam, J. Strathdee, Phys. Rev. D 2, 2869 (1970); J. Honerkamp, K. Meetz, Phys. Rev. D 3, 1996 (1971); J.M. Charap, Phys. Rev. D 3, 1998 (1971)
68. A. Salam, J. Strathdee, Phys. Rev. D 2, 2869 (1970); J. Honerkamp, K. Meetz, Phys. Rev. D 3, 1996 (1971); J.M. Charap, Phys. Rev. D 3, 1998 (1971)
69. A. Salam, J. Strathdee, Phys. Rev. D 2, 2869 (1970); J. Honerkamp, K. Meetz, Phys. Rev. D 3, 1996 (1971); J.M. Charap, Phys. Rev. D 3, 1998 (1971)
70. N.N. Bogoliubov, D.V. Shirkov, in Introduction to the theory of quantized fields (Interscience Publishers, Inc., New York 1959), pp. 136-153; p. 648
71. B. Klaiber, Helv. Phys. Acta 37, 554 (1964)