Methods of Contemporary Gauge Theory

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This book provides a thorough introduction to quantum theory of gauge fields. Emphasis is placed on four non-perturbative methods: path integrals, lattice gauge theories, the 1/N expansion, and reduced matrix models, which have important contemporary applications. The book uses a novel approach to gauge theories based on path-dependent phase factors known as the Wilson loops, and provides comprehensive coverage of large-N Yang-Mills theory.

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Editorial Reviews

From The Critics
A textbook for a graduate course on methods of contemporary gauge theory beyond the scope of perturbation theory. Students are assumed to be familiar with quantum mechanics and the standard methods of perturbative expansion in quantum field theory, particularly the theory of renormalization. Annotation c. Book News, Inc., Portland, OR
From the Publisher
' … the book is a valuable source of information on recent developments for advanced students.' Zentralblatt für Mathematik und ihre Grenzgebiete Mathematics Abstracts
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Product Details

Table of Contents

Pt. 1 Path Integrals 1
1 Operator calculus 3
2 Second quantization 35
3 Quantum anomalies from path integral 47
4 Instantons in quantum mechanics 65
Bibliography to Part 1 79
Pt. 2 Lattice Gauge Theories 83
5 Observables in gauge theories 85
6 Gauge fields on a lattice 99
7 Lattice methods 123
8 Fermions on a lattice 143
9 Finite temperatures 159
Bibliography to Part 2 179
Pt. 3 1/N Expansion 185
10 O(N) vector models 187
11 Multicolor QCD 213
12 QCD in loop space 249
13 Matrix models 287
Bibliography to Part 3 315
Pt. 4 Reduced Models 323
14 Eguchi-Kawai model 325
15 Twisted reduced models 351
16 Noncommutative gauge theories 377
Bibliography to Part 4 405
Index 411
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