Nonequilibrium quantum field theory

Bringing together the key ideas from nonequilibrium statistical mechanics and powerful methodology from quantum field theory, this book captures the essence of nonequilibrium quantum field theory. Beginning with the foundational aspects of the theory, the book presents important concepts and useful techniques, discusses issues of basic interest, and shows how thermal field, linear response, kinetic theories and hydrodynamics emerge. It also illustrates how these concepts and methodology are applied to current research topics including nonequilibrium phase transitions, thermalization in relativistic heavy ion collisions, the nonequilibrium dynamics of Bose-Einstein condensation, and the generation of structures from quantum fluctuations in the early Universe. Divided into five parts, each part addresses a particular stage in the conceptual and technical development of the subject.

Preface	p. xiii
I Fundamentals of Nonequilibrium Statistical Mechanics
1 Basic issues in nonequilibrium statistical mechanics	p. 3
1.1 Macroscopic description of physical processes	p. 4
1.2 Microscopic characterization from dynamical systems behavior	p. 11
1.3 Physical conditions	p. 16
1.4 Coarse graining and persistent structure in the physical world	p. 21
1.5 Physical systems: Closed, open, effectively closed and effectively open	p. 26
1.6 Appendix A: Stochastic processes and equations in a (tiny) nutshell	p. 31
2 Relaxation, dissipation, noise and fluctuations	p. 39
2.1 A simple model of Brownian motion	p. 39
2.2 The Fokker-Planck and Kramers-Moyal equations	p. 45
2.3 The Boltzmann equation	p. 49
3 Quantum open systems	p. 60
3.1 A quick review of quantum mechanics	p. 60
3.2 Influence functional	p. 68
3.3 The master equation	p. 72
3.4 The Langevin equation	p. 73
3.5 The Kramers-Moyal equation	p. 79
3.6 Derivation of the propagator and the master equation	p. 82
3.7 Consistent histories and decoherence functional	p. 86
II Basics of Nonequilibrium Quantum Field Theory
4 Quantum fields on time-dependent backgrounds: Particle creation	p. 93
4.1 Basic field theory	p. 94
4.2 Particle production in external fields	p. 106
4.3 Spontaneous and stimulated production	p. 111
4.4 Quantum Vlasov equation	p. 114
4.5 Periodically driven fields	p. 118
4.6 Particle creation in a dynamical spacetime	p. 121
4.7 Particle creation as squeezing	p. 131
4.8 Squeezed quantum open systems	p. 143
5 Open systems of interacting quantum fields	p. 148
5.1 Influence functional: Two interacting quantum fields	p. 149
5.2 Quantum functional master equation	p. 158
5.3 The closed time path coarse-grained effective action	p. 162
6 Functional methods in nonequilibrium QFT	p. 170
6.1 Propagators	p. 171
6.2 Functional methods	p. 174
6.3 The closed time path effective action	p. 180
6.4 Computing the closed time path effective action	p. 187
6.5 The two-particle irreducible effective action	p. 195
6.6 Handling divergences	p. 203
III Gauge Invariance, Dissipation, Entropy, Noise and Decoherence
7 Closed time path effective action for gauge theories	p. 211
7.1 Path integral quantization of gauge theories - an overview	p. 214
7.2 The 2PI formalism applied to gauge theories	p. 223
7.3 Gauge dependence and propagator structure	p. 226
8 Dissipation and noise in mean field dynamics	p. 231
8.1 Preliminaries	p. 234
8.2 Dissipation in the mean field dynamics	p. 235
8.3 Dissipation and particle creation	p. 236
8.4 Particle creation and noise	p. 238
8.5 Full quantum correlations from the Langevin approach	p. 240
8.6 The fluctuation-dissipation theorem	p. 242
8.7 Particle creation and decoherence	p. 243
8.8 The nonlinear regime	p. 244
8.9 Final remarks	p. 249
9 Entropy generation and decoherence of quantum fields	p. 251
9.1 Entropy generation from particle creation	p. 251
9.2 Entropy of quantum fields	p. 255
9.3 Entropy from the (apparent) damping of the mean field	p. 258
9.4 Entropy of squeezed quantum open systems	p. 262
9.5 Decoherence in a quantum phase transition	p. 270
9.6 Spinodal decomposition of an interacting quantum field	p. 274
9.7 Decoherence of the inflaton field	p. 281
IV Thermal, Kinetic and Hydrodynamic Regimes
10 Thermal field and linear response theory	p. 291
10.1 The thermal generating functional	p. 291
10.2 Linear response theory	p. 293
10.3 The Kubo-Martin-Schwinger theorem	p. 294
10.4 Thermal self-energy: Screening	p. 297
10.5 Landau damping	p. 298
10.6 Hard thermal loops	p. 305
11 Quantum kinetic field theory	p. 315
11.1 The Kadanoff-Baym equations	p. 315
11.2 Quantum kinetic field theory on nontrivial backgrounds	p. 330
12 Hydrodynamics and thermalization	p. 345
12.1 Classical relativistic hydrodynamics	p. 346
12.2 Quantum fields in the hydrodynamic limit	p. 353
12.3 Transport functions in the hydrodynamic limit	p. 360
12.4 Transport functions from linear response theory	p. 367
12.5 Thermalization	p. 374
V Applications to Selected Current Research
13 Nonequilibrium Bose-Einstein condensates	p. 391
13.1 The closed time path integral approach to BECs	p. 393
13.2 The symmetry-breaking approach to BECs	p. 396
13.3 The particle number conserving formalism	p. 420
14 Nonequilibrium issues in RHICs and DCCs	p. 429
14.1 Relativistic heavy ion collisions (RHICs)	p. 429
14.2 Disoriented chiral condensates (DCCs)	p. 439
15 Nonequilibrium quantum processes in the early universe	p. 447
15.1 Quantum fluctuations and noise in inflationary cosmology	p. 448
15.2 Structure formation: Effect of colored noise	p. 457
15.3 Reheating in the inflationary universe	p. 474
References	p. 490
Index	p. 530

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