Methods of contemporary gauge theory / Yuri Makeenko.

Format:

Book

Author/Creator:

Makeenko, Yuri, 1951-

Contributor:

Alumni and Friends Memorial Book Fund.

Series:

Cambridge monographs on mathematical physics

Language:

English

Subjects (All):

Gauge fields (Physics).

Mathematical physics.

Physical Description:

xii, 417 pages : illustrations ; 26 cm.

Place of Publication:

Cambridge ; New York : Cambridge University Press, 2002.

Summary:

Thorough introduction to quantum theory of gauge fields, with emphasis on modern non-perturbative methods.

Contents:

Part 1 Path Integrals 1

1 Operator calculus 3

1.1 Free propagator 3

1.2 Euclidean formulation 6

1.3 Path-ordering of operators 10

1.4 Feynman disentangling 13

1.5 Calculation of the Gaussian path integral 18

1.6 Transition amplitudes 20

1.7 Propagators in external field 29

2 Second quantization 35

2.1 Integration over fields 35

2.2 Grassmann variables 37

2.3 Perturbation theory 38

2.4 Schwinger-Dyson equations 40

2.5 Commutator terms 40

2.6 Schwinger-Dyson equations (continued) 41

2.7 Regularization 45

3 Quantum anomalies from path integral 47

3.1 QED via path integral 47

3.2 Chiral Ward identity 48

3.3 Chiral anomaly 51

3.4 Chiral anomaly (calculation) 55

3.5 Scale anomaly 59

4 Instantons in quantum mechanics 65

4.1 Double-well potential 65

4.2 The instanton solution 68

4.3 Instanton contribution to path integral 70

4.4 Symmetry restoration by instantons 75

4.5 Topological charge and [theta]-vacua 76

Part 2 Lattice Gauge Theories 83

5 Observables in gauge theories 85

5.1 Gauge invariance 85

5.2 Phase factors (definition) 88

5.3 Phase factors (properties) 93

5.4 Aharonov-Bohm effect 95

6 Gauge fields on a lattice 99

6.1 Sites, links, plaquettes and all that 100

6.2 Lattice formulation 102

6.3 The Haar measure 107

6.4 Wilson loops 110

6.5 Strong-coupling expansion 113

6.6 Area law and confinement 117

6.7 Asymptotic scaling 119

7 Lattice methods 123

7.1 Phase transitions 124

7.2 Mean-field method 128

7.3 Mean-field method (variational) 131

7.4 Lattice renormalization group 133

7.5 Monte Carlo method 136

7.6 Some Monte Carlo results 140

8 Fermions on a lattice 143

8.1 Chiral fermions 143

8.2 Fermion doubling 145

8.3 Kogut-Susskind fermions 151

8.4 Wilson fermions 152

8.5 Quark condensate 156

9 Finite temperatures 159

9.1 Feynman-Kac formula 160

9.2 QCD at finite temperature 166

9.3 Confinement criterion at finite temperature 168

9.4 Deconfining transition 170

9.5 Restoration of chiral symmetry 175

Part 3 1/N Expansion 185

10 O(N) vector models 187

10.1 Four-Fermi theory 188

10.2 Bubble graphs as the zeroth order in 1/N 191

10.3 Functional methods for [open phi superscript 4] theory 200

10.4 Nonlinear sigma model 208

10.5 Large-N factorization in vector models 211

11 Multicolor QCD 213

11.1 Index or ribbon graphs 214

11.2 Planar and nonplanar graphs 218

11.3 Planar and nonplanar graphs (the boundaries) 224

11.4 Topological expansion and quark loops 230

11.5 't Hooft versus Veneziano limits 233

11.6 Large-N factorization 237

11.7 The master field 243

11.8 1/N as semiclassical expansion 246

12 QCD in loop space 249

12.1 Observables in terms of Wilson loops 249

12.2 Schwinger-Dyson equations for Wilson loop 255

12.3 Path and area derivatives 258

12.4 Loop equations 263

12.5 Relation to planar diagrams 267

12.6 Loop-space Laplacian and regularization 269

12.7 Survey of nonperturbative solutions 274

12.8 Wilson loops in QCD[subscript 2] 275

12.9 Gross-Witten transition in lattice QCD[subscript 2] 282

13 Matrix models 287

13.1 Hermitian one-matrix model 288

13.2 Hermitian one-matrix model (solution at N = [infinity]) 294

13.3 The loop equation 297

13.4 Solution in 1/N 300

13.5 Continuum limit 303

13.6 Hermitian multimatrix models 311

Part 4 Reduced Models 323

14 Eguchi-Kawai model 325

14.1 Reduction of the scalar field (lattice) 325

14.2 Reduction of the scalar field (continuum) 330

14.3 Reduction of the Yang-Mills field 332

14.4 The continuum Eguchi-Kawai model 336

14.5 R[superscript d] symmetry in perturbation theory 340

14.6 Quenched Eguchi-Kawai model 342

15 Twisted reduced models 351

15.1 Twisting prescription 351

15.2 Twisted reduced model for scalars 355

15.3 Twisted Eguchi-Kawai model 362

15.4 Twisting prescription in the continuum 368

15.5 Continuum version of TEK 372

16 Noncommutative gauge theories 377

16.1 The noncommutative space 378

16.2 The U[subscript [theta](1) gauge theory 383

16.3 One-loop renormalization 386

16.4 Noncommutative quantum electrodynamics 389

16.5 Wilson loops and observables 391

16.6 Compactification to tori 396

16.7 Morita equivalence 401.

Notes:

Includes bibliographical references (pages 405-410) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Alumni and Friends Memorial Book Fund.

ISBN:

0521809118

OCLC:

48931615

Online:

Publisher description