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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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Non-Abelian Gauge Theories: Introduction

Non-Abelian Gauge Theories: Introduction

Quantum Field Theory and Critical Phenomena


Oxford University Press

This chapter constructs a field theory invariant under local, that is, space-dependent, transformations of a general compact Lie group G. Inspired by the abelian example of Chapter 18, it introduces the geometric concept of parallel transport — a concept discussed more extensively in Chapter 22 in the example of Riemannian manifolds. All the required mathematical quantities then appear quite naturally. It quantizes gauge theories and studies some of the formal properties of the quantum theory like the BRS symmetry. The chapter shows how perturbation theory can be regularized, a somewhat non-trivial problem. Finally, it discusses general aspects of the Higgs mechanism.

Keywords:   field theory, Lie group, parallel transport, perturbation theory, Higgs mechanism

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