Abstract
The phenomena of electroweak phase transitions in the early universe depend crucially on the inclusion of the charge corresponding to the spontaneously broken symmetry, which is usually taken as classically conserved. This paper is devoted to the study of the electroweak phase transitions at high temperatures and, correspondingly, to the controversy in the literature concerning the question of the inclusion of the weak neutral charge in the standard model, for the investigation of the phase transition ofW-boson condensation and symmetry restoration in the early universe. Several arguments, general and perturbative, are given against the introduction of the weak neutral charge conservation in the nonsymmetric phase. As a consequence of the above, theW-condensation should occur even at low lepton densities and the symmetry restoration critical curve is independent of the lepton density. The use of different gauges such as the renormalizable and the unitary ones is also discussed.
Similar content being viewed by others
References
D.A. Kirzhnitz, A.D. Linde: Phys. Lett. 42B (1972) 471; Ann. Phys. 101 (1976) 195
O.K. Kalashnikov, H. Perez Rojas: Kratkie Soob. po Fizike, Lebedev Institute Reports, Allerton Press N.2 (1986) 23; H. Perez Rojas, O.K. Kalashnikov: Nucl. Phys. B293 (1987) 241
A.D. Linde: Phys. Lett. 85B (1979) 39
E.J. Ferrer, V. de la Incera, A.E. Shabad: Phys. Lett. B185 (1987) 407; E.J. Ferrer, V. de la Incera, A.E. Shabad: Nucl. Phys. B309 (1988) 120
O.K. Kalashnikov, H. Perez Rojas: Phys. Rev. D40 (1989) 1255
H. Perez Rojas, R. Torres Rivero: Phys. Lett. A137 (1989) 13
J. Kapusta: Phys. Rev. D 42 (1990) 919
M. Chaichian, C. Montonen, H. Perez Rojas: Phys. Lett. B 256 (1991) 227; M. Chaichian, J. Gonzalez, C. Montonen, H. Perez Rojas: Phys. Lett. B 300 (1993) 118; E.S. Fradkin, I.V. Tyutin: Riv. Nuovo Cimento 4 (1979) 1
S. Coleman: J. Math. Phys. 7, 5 (1966) 787
J. Goldstone: Nuovo Cimento 19 (1961) 154; J. Goldstone, A. Salam, S. Weinberg: Phys. Rev. 127, 3 (1962) 965
R. Haag: Nuovo Cimento 25 (1962) 287
C. Orzalezi: Rev. Mod. Phys. 42 (1970) 381
H. Araki, D. Kastler, M. Takesaki, R. Haag: Commun. Math. Phys. 53 (1977) 97
N.K. Nielsen: Nucl. Phys. B 101 (1975) 173; I.J.R. Aitchison, C.M. Fraser: Ann. Phys. 156 (1984) 1
R. Fukuda, T. Kugo: Phys. Rev. D 13 (1976) 3469
B.S. DeWitt: in: Quantum gravity II. Oxford: Oxford University, Press 1981
D.G. Boulware: Phys. Rev. D 23 (1981) 389
L.D. Dolan, R. Jackiw: Phys. Rev. D9 (1974) 3320
S. Weinberg: Phys. Rev. D9 (1974) 3357
R.J. Rivers: J. Phys. C 22 (1984) 137; D. Johnston: J. Phys. C 31 (1986) 129
For a comprehensive account of inadequacy of unitary gauge within the effective potential approach, i.e. off mass-shell, see: M. Chaichian, E.J. Ferrer, V. de la Incera: Nucl. Phys. B. 362 (1991) 616
A.D. Linde: Rep. Prog. Phys., 42 (1979) 389
W. Buchmuller, Z. Fodor; Preprint DESY 93-032, 1993; W. Buchmuller, Z. Fodor, T. Helbig, D. Walliser: Preprint DESY 93-021, 1993; J.R. Espinosa, M. Quiros, F. Zwirner: Preprint CERN-TH 6577/92, 1992
H.E. Haber, H.A. Weldon: Phys. Rev. 25D (1982) 502; H. Perez Rojas: Cien. Tee. Fis. Mat. 7 (1987) 60
L.P. Horwitz, S. Raby: Phys. Rev. D15 (1977) 1772; J. Bros, D. Buchholz, V. Glaser: Commun. Math. Phys. 50 (1976) 11; E. Gal-Ezer, H. Reeh: Commun. Math. Phys. 43 (1975) 137, J. Bernstein: Rev. Mod. Phys. 46 (1974) 7
J.R. Espinosa, M. Quiros, F. Zwirner: Phys. Lett. B307 (1993) 106.
J. Bernstein, S. Dodelson: Phys. Rev. Lett. 66 (1991) 683
S. Mohan: Phys. Lett. B307 (1993) 367
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chaichian, M., Gonzalez Felipe, R., Louis Martinez, D. et al. Chemical potentials and high temperature phase transitions in electroweak theory. Z. Phys. C - Particles and Fields 64, 95–104 (1994). https://doi.org/10.1007/BF01557240
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01557240