Jump to ContentJump to Main Navigation
Quantum Field Theory and Critical Phenomena$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 18 June 2019

Abelian Gauge Theories

Abelian Gauge Theories

Chapter:
(p.448) 18 ABELIAN GAUGE THEORIES
Source:
Quantum Field Theory and Critical Phenomena
Author(s):

JEAN ZINN-JUSTIN

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198509233.003.0018

This chapter focuses on abelian gauge theory, whose physical realization is Quantum Electrodynamics (QED). The chapter is organized as follows. It begins with elementary considerations about the massive vector field in perturbation theory. It shows that coupling to matter field leads to field theories that are renormalizable in four dimensions only if the vector field is coupled to a conserved current. In the latter case the massless vector limit can be defined. The corresponding field theories are gauge invariant. It then discusses the specific properties of gauge invariant theories and mentions the IR problem of physical observables. It quantizes gauge theories starting directly from first principles. The formal equivalence between different gauges is established. Regularization methods are presented which allow overcoming the new diffculties one encounters in gauge theories. The abelian gauge symmetry, broken by gauge fixing terms, then leads to a set of WT identities which are used to prove the renormalizability of the theory. The gauge dependence of correlation functions in a set of covariant gauges is determined. Renormalization group equations follow and the RG β-function is calculated at leading order. As an introduction to the next chapter, the abelian Higgs mechanism is analyzed. Finally, the chapter comments about stochastic quantization of gauge theories.

Keywords:   abelian gauge theory, perturbation theory, gauge invariance, WT identities, renormalization, Higgs mechanism

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .