Methods of Contemporary Gauge Theory

Yuri Makeenko

doi:10.1017/9781009402095

This book introduces the quantum theory of gauge fields, emphasising four non-perturbative methods which have important applications: path integrals, lattice gauge theories, the 1/N expansion, and reduced matrix models. Written as a textbook, it assumes a knowledge of quantum mechanics and elements of perturbation theory, while many relevant concepts are introduced at a basic level in the first half of the book. The second half comprehensively covers large-N Yang–Mills theory. The book uses an approach to gauge theories based on path-dependent phase factors known as Wilson loops, and contains problems with detailed solutions to aid understanding. Suitable for advanced graduate courses in quantum field theory, the book will also be of interest to researchers in high energy theory and condensed matter physics as a survey of recent developments in gauge theory. Originally published in 2002, this title has been reissued as an Open Access publication on Cambridge Core.

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Contents

Frontmatter
pp i-vi
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Contents
pp vii-x
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Preface
pp xi-xii
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Part 1: - Path Integrals
pp 1-2
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1 - Operatorcalculus
pp 3-34
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2 - Second quantization
pp 35-46
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3 - Quantum anomalies from path integral
pp 47-64
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4 - Instantons in quantum mechanics
pp 65-82
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Part 2: - Lattice Gauge Theories
pp 83-84
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5 - Observables in gauge theories
pp 85-98
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6 - Gauge fields on a lattice
pp 99-122
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7 - Lattice methods
pp 123-142
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8 - Fermions on a lattice
pp 143-158
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9 - Finite temperatures
pp 159-184
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Part 3: - 1/N Expansion
pp 185-186
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10 - O(N) vector models
pp 187-212
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11 - Multicolor QCD
pp 213-248
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12 - QCD in loop space
pp 249-286
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13 - Matrix models
pp 287-322
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Part 4: - Reduced Models
pp 323-324
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14 - Eguchi–Kawai model
pp 325-350
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15 - Twisted reduced models
pp 351-376
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16 - Noncommutative gauge theories
pp 377-410
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Index
pp 411-418
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Methods of Contemporary Gauge Theory

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Contents

Frontmatter
pp i-vi

Contents
pp vii-x

Preface
pp xi-xii

Part 1: - Path Integrals
pp 1-2

1 - Operatorcalculus
pp 3-34

2 - Second quantization
pp 35-46

3 - Quantum anomalies from path integral
pp 47-64

4 - Instantons in quantum mechanics
pp 65-82

Part 2: - Lattice Gauge Theories
pp 83-84

5 - Observables in gauge theories
pp 85-98

6 - Gauge fields on a lattice
pp 99-122

7 - Lattice methods
pp 123-142

8 - Fermions on a lattice
pp 143-158

9 - Finite temperatures
pp 159-184

Part 3: - 1/N Expansion
pp 185-186

10 - O(N) vector models
pp 187-212

11 - Multicolor QCD
pp 213-248

12 - QCD in loop space
pp 249-286

13 - Matrix models
pp 287-322

Part 4: - Reduced Models
pp 323-324

14 - Eguchi–Kawai model
pp 325-350

15 - Twisted reduced models
pp 351-376

16 - Noncommutative gauge theories
pp 377-410

Index
pp 411-418

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Methods of Contemporary Gauge Theory

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