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: 21 May 2019

Gauge Theories: Master Equation And Renormalization

Gauge Theories: Master Equation And Renormalization

Chapter:
(p.532) 21 GAUGE THEORIES: MASTER EQUATION AND RENORMALIZATION
Source:
Quantum Field Theory and Critical Phenomena
Author(s):

JEAN ZINN-JUSTIN

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198509233.003.0021

To discuss the renormalization of gauge theories in the non-abelian case in its full generality, it is necessary to use a rather abstract formalism, which allows one to understand the algebraic structure of the renormalization procedure without being overwhelmed by the notational complexity. There is, however, a price to pay: the translation of the general identities which then appear into usual and more concrete notation becomes a non-trivial exercise. This chapter is organized as follows. It first quantizes the theory in the temporal gauge. Using a simple identity, it shows the equivalence with a quantization in a general class of gauges. This identity automatically implies a BRS symmetry, and, therefore, a set of WT identities for correlation functions. It shows that WT identities are also direct consequences of a quadratic master equation satisfied the quantized action, equation in which gauge and BRS symmetries are no longer explicit. It shows that in the case of renormalizable gauges the master equation is stable under renormalization. This is solved to determine the structure of the renormalized action. The chapter verifies that the master equation encodes in a subtle way the gauge properties of the quantized action.

Keywords:   gauge theories, quantization, quadratic master equation, renormalization

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 .