Abstract
We give a review (and some improvements) of the rigorous results on the phase structure of Abelian lattice Higgs models with gauge groups U(1) and ℝ. Emphasis is put on the relation between the Higgs mechanism (gauge-independent) and spontaneous symmetry breaking (gauge-dependent). We also discuss some nonperturbative effects due to Gribov copies in this context.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Brydges, J. Fröhlich, and E. Seiler,Nucl. Phys. B 152:521 (1979).
D. Brydges and E. Seiler,J. Stat. Phys. 42:405 (1986).
C. Borgs and F. Nill,Phys. Lett. B 171:289 (1986).
T. Balaban, D. Brydges, J. Imbrie, and A. Jaffe,Ann. Phys. 158:281 (1984).
J. Bernstein,Rev. Mod. Phys. 46:7 (1974).
S. Elitzur,Phys. Rev. D 12:3978 (1975); G. F. De Angelis, D. de Falco, and F. Guerra,Phys. Rev. D 17:1624 (1978).
T. Kennedy and C. King,Commun. Math. Phys. 104:327 (1986).
C. Borgs and F. Nill,Commun. Math. Phys. 104:349 (1986).
B. W. Lee,Phys. Rev. D 5:823 (1972).
N. D. Mermin and H. Wagner,Phys. Rev. Lett. 17:1133 (1966); S. Coleman,Commun. Math. Phys. 31:259 (1973).
O. McBryan and T. Spencer,Commun. Math. Phys. 53:299 (1977).
C. Borgs and F. Nill,Nucl. Phys. B 270[FS 16]:92 (1986).
F. Nill, Ph.D. Thesis, Ludwig-Maximilans-Universität München, Max-Planck preprint MPI-PAE/PTh 31/87.
F. Nill, Preprint MPI-PAE/PTh 39/85; Faddeev-Popov trick, loop expansion and spontaneous symmetry breaking in the presence of Gribov copies—A differential geometric survey, Invited talk, XVth International Conference on Differential Geometry Methods in Theoretical Physics, Clausthal 1986, Proceedings to appear.
B. Sharpe,J. Math. Phys. 25:3324 (1985).
J. Jersák, Lattice Higgs models,in Lattice Gauge Theory—A Challenge in Large-Scale Computing (Wuppertal, 1985), B. Bunk, K. H. Mütter, and K. Schilling, eds., (Plenum Press, New York, 1986).
K. Fredenhagen and M. Marcu,Commun. Math. Phys. 92:81 (1983);Phys. Rev. Lett. 56:223 (1986); K. Kondo,Progr. Theor. Phys. 74:152 (1985); J. C. A. Barata and W. F. Wreszinski,Commun. Math. Phys. 103:637 (1986).
J. Fröhlich and P. A. Marchetti,Europhys. Lett. 2:933 (1986).
J. Bricmont and J. Fröhlich,Phys. Lett. B 122:73 (1983);Nucl. Phys. B 251[FS 13]:517 (1985);Commun. Math. Phys. 98:553 (1985); ETH-Preprint (1986), to appear inNucl. Phys. B.
A. Guth,Phys. Rev. D 21:2291 (1980).
D. Brydges, J. Fröhlich, and E. Seiler,Ann. Phys. 121:227 (1979).
E. Seiler,Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics (Springer, Berlin, 1982).
K. Osterwalder and E. Seiler,Ann. Phys. 110:440 (1978).
C. King,Commun. Math. Phys. 104:675 (1986).
J. Fröhlich and T. Spencer,Commun. Math. Phys. 83:411 (1982).
P. L. Dobrushin,Theor. Prob. Appl. 13:197 (1968); O. Lanford and D. Ruelle,Commun. Math. Phys. 13:194 (1969).
K. Szlachányi,Commun. Math. Phys. 108:319 (1987).
D. C. Brydges, A short course on cluster expansions, Les Houches Lectures (1984).
D. Brydges, J. Fröhlich, and T. Spencer,Commun. Math. Phys. 83:123 (1982).
Author information
Authors and Affiliations
Additional information
This paper is based on an invited talk given by one of the authors (C.B.) at the conference on the Statistical Mechanics of Phase Transitions—Mathematical and Physical Aspects, Třeboň, Czechoslovakia, September 1–6, 1986.
Rights and permissions
About this article
Cite this article
Borgs, C., Nill, F. The phase diagram of the Abelian lattice Higgs model. A review of rigorous results. J Stat Phys 47, 877–904 (1987). https://doi.org/10.1007/BF01206163
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01206163