Document Zbl 0593.46061

Spontaneous symmetry breakdown in the abelian Higgs model. (English) Zbl 0593.46061

Commun. Math. Phys. 104, 327-347 (1986).

Summary: For the abelian Higgs model we introduce a new gauge invariant observable which in Landau gauge is \(\phi\) (x)\({\bar \phi}\)(y). In three or more dimensions this observable is used to show that the global gauge symmetry is spontaneously broken in the lattice theory for a suitable range of parameters. This observable also provides a gauge invariant order parameter for the phase transition in this model.

Cited in 1 Review

Cited in 18 Documents

MSC:

46N99	Miscellaneous applications of functional analysis
53B50	Applications of local differential geometry to the sciences
81T08	Constructive quantum field theory

Keywords:

abelian Higgs model; gauge invariant observable; Landau gauge; global gauge symmetry; gauge invariant order parameter

Citations:

Zbl 0593.46062

Cite Review PDF

Full Text: DOI

References:

[1]	Ba?aban, T., Brydges, D., Imbrie, J., Jaffe, A.: The mass gap for Higgs models on a unit lattice. Ann. Phys.158, 281-319 (1984) · Zbl 0583.46060 · doi:10.1016/0003-4916(84)90121-0
[2]	Bernstein, J.: Spontaneous symmetry breaking, gauge theories, the Higgs mechanism and all that. Rev. Mod. Phys.46, 7-48 (1974) · doi:10.1103/RevModPhys.46.7
[3]	Bricmont, J., Fröhlich, J.: An order parameter distinguishing between different phases of lattice gauge theories with matter fields. Phys. Lett.122 B, 73-77 (1983)
[4]	Bricmont, J., Lebowitz, J.L., Pfister, C.-E.: Periodic Gibbs states of ferromagnetic spin systems. J. Stat. Phys.24, 269-277 (1981) · doi:10.1007/BF01007648
[5]	Brydges, D.: A short course on cluster expansions. In: Proceedings of 1984 Les Houches summer school. Osterwalder, K. (ed.) (to be published) · Zbl 0659.60136
[6]	Brydges, D., Fröhlich, J., Seiler, E.: On the construction of quantized gauge fields. I. General results. Ann. Phys.121, 227-284 (1979) · doi:10.1016/0003-4916(79)90098-8
[7]	Brydges, D., Fröhlich, J., Seiler, E.: Diamagnetism and critical properties of Higgs lattice gauge theories. Nucl. Phys. B152, 521-532 (1979) · doi:10.1016/0550-3213(79)90095-6
[8]	Brydges, D., Seiler, E.: Absence of screening in certain lattice gauge and plasma models. Princeton University preprint
[9]	Drühl, K., Wagner, H.: Algebraic formulation of duality transformations for abelian lattice models. Ann. Phys.141, 225-253 (1982) · doi:10.1016/0003-4916(82)90286-X
[10]	Fröhlich, J., Morchio, G., Strocchi, F.: Higgs phenomenon without symmetry breaking order parameter. Nucl. Phys. B190, 553-582 (1981) · doi:10.1016/0550-3213(81)90448-X
[11]	Fröhlich, J., Simon, B., Spencer, T.: Infrared bounds, phase transitions and continuous symmetry breaking. Commun. Math. Phys.50, 79-95 (1976) · doi:10.1007/BF01608557
[12]	Fröhlich, J., Spencer, T.: Massless phases and symmetry restoration in abelian gauge theories and spin systems. Commun. Math. Phys.83, 411-454 (1982) · doi:10.1007/BF01213610
[13]	Fredenhagen, K., Marcu, M.: Charged states in ?2 gauge theories. Commun. Math. Phys.92, 81-119 (1983) · Zbl 0535.46052 · doi:10.1007/BF01206315
[14]	Fredenhagen, K., Marcu, M.: A confinement criterion for QCD with dynamical quarks, DESY preprint 85-008
[15]	Guth, A.: Existence proof of a nonconfining phase in four dimensional U(1) lattice gauge theory. Phys. Rev. D21, 2291-2307 (1980)
[16]	Kennedy, T., King, C.: Symmetry breaking in the lattice abelian Higgs model. Phys. Rev. Lett.55, 776-778 (1985) · doi:10.1103/PhysRevLett.55.776
[17]	McBryan, O., Spencer, T.: On the decay of correlations in SO(n)-symmetric ferromagnets. Commun. Math. Phys.53, 299-302 (1977) · doi:10.1007/BF01609854
[18]	Osterwalder, K., Seiler, E.: Gauge field theories on a lattice. Ann. Phys.110, 440-471 (1978) · doi:10.1016/0003-4916(78)90039-8
[19]	Seiler, E.: Gauge theories as a problem of constructive quantum field theory and statistical mechanics. Lecture Notes in Physics, Vol. 159. Berlin, Heidelberg, New York: Springer 1982
[20]	Wells, D.: Thesis, Indiana University (1977)

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.