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Quantum Field Theory and Critical Phenomena$
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Jean Zinn-Justin

Print publication date: 2002

Print ISBN-13: 9780198509233

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198509233.001.0001

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Critical Properties Of Gauge Theories

Critical Properties Of Gauge Theories

Quantum Field Theory and Critical Phenomena


Oxford University Press

This chapter considers lattice models with gauge symmetry and discusses their properties from the point of view of phase transitions and spectrum structure. It focuses on pure lattice gauge theories (without fermions) and studies them mainly with lattice methods. The chapter first constructs lattice models with gauge symmetry. It shows that they provide a lattice regularization of the continuum gauge theories studied in Chapters18-21: the low temperature or small coupling expansion of the lattice model is a regularized continuum perturbation theory. It then discusses pure gauge theories (without matter fields) on the lattice. It discovers that gauge theories have properties quite different from the ferromagnetic systems studied so far. In particular, the absence of a local order parameter will force us to examine the behaviour of a non-local quantity, a functional of loops called hereafter Wilson's loop to distinguish between the confined and deconfined phases. Results will be obtained in the high temperature or strong coupling limit and in the mean field approximation.

Keywords:   lattice models, gauge symmetry, phase transitions, Wilson's loop, mean field approximation

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