Finite-temperature field theory: principles and applications

Half-title......Page 3
Series-title......Page 4
Title......Page 5
Copyright......Page 6
Contents......Page 7
1.1 Ensembles......Page 15
1.2 One bosonic degree of freedom......Page 17
1.3 One fermionic degree of freedom......Page 19
1.4 Noninteracting gases......Page 20
1.5 Exercises......Page 24
Numerical evaluation of thermodynamic integrals......Page 25
2.1 Transition amplitude for bosons......Page 26
2.2 Partition function for bosons......Page 29
2.3 Neutral scalar field......Page 30
2.4 Bose–Einstein condensation......Page 33
2.5 Fermions......Page 37
2.6 Remarks on functional integrals......Page 44
Functional integrals in field theory at finite temperature......Page 45
Grassmann variables......Page 46
3.1 Perturbation expansion......Page 47
3.2 Diagrammatic rules for LambdaPhi theory......Page 48
3.3 Propagators......Page 52
3.4 First-order corrections to Pi and ln Z......Page 55
3.5 Summation of infrared divergences......Page 59
3.6 Yukawa theory......Page 61
3.7 Remarks on real time perturbation theory......Page 65
3.8 Exercises......Page 67
Ring diagram contribution......Page 68
4.1 Renormalizing LambdaPhi theory......Page 69
4.2 Renormalization group......Page 71
4.3 Regularization schemes......Page 74
4.4 Application to the partition function......Page 75
Renormalization group and high temperature......Page 77
5.1 Quantizing the electromagnetic field......Page 78
5.2 Blackbody radiation......Page 82
5.3 Diagrammatic expansion......Page 84
5.4 Photon self-energy......Page 85
5.5.1 Two loops......Page 88
5.5.2 Ring diagrams......Page 91
5.5.3 Three loops at finite density......Page 94
5.5.4 Three loops at finite temperature......Page 95
5.6 Exercises......Page 96
Relativistic QED at finite temperature and density......Page 97
6.1 Linear response to an external field......Page 98
6.2 Lehmann representation......Page 101
6.3 Screening of static electric fields......Page 104
6.4 Screening of a point charge......Page 108
6.5 Exact formula for screening length in QED......Page 111
6.6 Collective excitations......Page 114
6.7 Photon dispersion relation......Page 115
6.8 Electron dispersion relation......Page 119
6.9 Kubo formulae for viscosities and conductivities......Page 121
6.10 Exercises......Page 128
Linear response theory......Page 129
Kubo-type relations and hydrodynamics......Page 130
7.1 Charged scalar field with negative mass-squared......Page 131
7.2 Goldstone’s theorem......Page 137
7.3 Loop corrections......Page 139
7.4 Higgs model......Page 144
References......Page 147
Thermodynamics......Page 148
8 Quantum chromodynamics......Page 149
8.1 Quarks and gluons......Page 150
8.2 Asymptotic freedom......Page 153
8.3 Perturbative evaluation of partition function......Page 160
8.4 Higher orders at finite temperature......Page 163
8.5 Gluon propagator and linear response......Page 166
8.6 Instantons......Page 170
8.7 Infrared problems......Page 175
8.8 Strange quark matter......Page 177
8.9 Color superconductivity......Page 180
8.10 Exercises......Page 188
References......Page 189
Reviews of QCD (at zero and finite temperature)......Page 190
9 Resummation and hard thermal loops......Page 191
9.1 Isolating the hard thermal loop contribution......Page 193
9.2 Hard thermal loops and Ward identities......Page 199
9.3 Hard thermal loops and effective perturbation theory......Page 201
9.4 Spectral densities......Page 202
9.5 Kinetic theory......Page 203
9.6 Transport coefficients......Page 207
References......Page 208
10 Lattice gauge theory......Page 209
10.1 Abelian gauge theory......Page 210
10.2 Nonabelian gauge theory......Page 216
10.3 Fermions......Page 217
10.4 Phase transitions in pure gauge theory......Page 220
10.5 Lattice QCD......Page 226
References......Page 231
Bibliography......Page 232
11 Dense nuclear matter......Page 233
11.1 Walecka model......Page 234
11.2 Loop corrections......Page 240
11.2.1 Relativistic Hartree......Page 241
11.2.2 Two loops......Page 242
11.2.3 Form factors......Page 243
11.3 Three- and four-body interactions......Page 246
11.4 Liquid–gas phase transition......Page 247
11.5 Summary......Page 250
11.6 Exercises......Page 251
References......Page 252
Relativistic nuclear field theories......Page 253
12.1 Chiral perturbation theory......Page 254
12.2 Self-energy from experimental data......Page 262
12.3.1 Sum rules at zero temperature......Page 268
12.3.2 Sum rules at finite temperature......Page 271
Low-temperature behavior......Page 276
The approach to chiral-symmetry restoration......Page 277
12.4.1 Linear σ model at finite temperature......Page 279
12.4.2 Nonlinear Sigma model at finite temperature......Page 284
12.4.3 Finite-temperature behavior of fπ......Page 291
The nonlinear Sigma model......Page 293
The linear Sigma model......Page 296
12.4.4 Finite-temperature scalar condensate......Page 298
References......Page 301
The operator product expansion and its application to QCD......Page 302
13 Nucleation theory......Page 303
13.1 Quantum nucleation......Page 304
13.2 Classical nucleation......Page 308
13.3 Nonrelativistic thermal nucleation......Page 310
13.4 Relativistic thermal nucleation......Page 312
13.4.1 Relativistic fluid dynamics......Page 314
13.4.2 Parametrization of the free energy......Page 316
13.4.3 Surface profile......Page 317
13.4.4 The prefactor......Page 320
13.5 Black hole nucleation......Page 327
References......Page 329
Bibliography......Page 330
14 Heavy ion collisions......Page 331
14.1 Bjorken model......Page 332
14.2 The statistical model of particle production......Page 338
14.3 The emission of electromagnetic radiation......Page 342
14.4 Photon production in high-energy heavy ion collisions......Page 345
14.5 Dilepton production......Page 353
14.6 J/Psi suppression......Page 359
14.7 Strangeness production......Page 364
14.8 Exercises......Page 370
References......Page 372
A reprint volume containing many of the pioneering papers on relativistic heavy ion collisions......Page 373
A series of international conferences on the subject of relativistic heavy ion collisions:......Page 374
15.1 Glashow–Weinberg–Salam model......Page 375
15.2 Symmetry restoration in mean field approximation......Page 379
15.3 Symmetry restoration in perturbation theory......Page 383
15.4 Symmetry restoration in lattice theory......Page 388
References......Page 391
Dimensional reduction and its use in electroweak lattice calculations......Page 392
16 Astrophysics and cosmology......Page 393
16.1 White dwarf stars......Page 394
16.2 Neutron stars......Page 396
16.3 Neutrino emissivity......Page 402
16.3.1 Pair annihilation......Page 403
16.3.2 Plasma decay......Page 404
16.3.3 Direct Urca process for quarks......Page 406
16.4.1 Inhomogeneous big bang nucleosynthesis......Page 408
16.4.2 Dynamics of the phase transition......Page 410
16.5 Electroweak phase transition and baryogenesis......Page 416
16.6 Decay of a heavy particle......Page 422
16.7 Exercises......Page 424
References......Page 425
Newborn neutron stars......Page 426
Conclusion......Page 427
A1.1 Thermodynamic relations......Page 431
A1.2 Microcanonical and canonical ensembles......Page 432
A1.3 High-temperature expansions......Page 435
A1.4 Expansion in the degeneracy......Page 437
References......Page 438
Index......Page 439