Preface ...................................................... xiii
Notation ....................................................... XV
1 Free Fields in Vacuum ........................................ 1
1.1 Generalities ............................................ 1
1.2 Scalar Field ............................................ 3
1.3 Dirac Field ............................................. 6
1.4 Vector Field ............................................ 8
1.5 Rarita-Schwinger Field ................................. 10
1.6 General Fields ......................................... 12
Problems .................................................... 14
References .................................................. 19
2 Spontaneous Symmetry Breaking ............................... 21
2.1 Linear cr-Models ....................................... 21
2.2 Goldstone Theorem (First Proof) ........................ 26
2.3 Goldstone Theorem (Second Proof) ....................... 30
2.4 Other Matrix Elements of Current ....................... 34
2.5 Linear u-Model Revisited ............................... 38
2.6 Non-Linear a-Model ..................................... 40
2.7 Effective Field Theories ............................... 42
2.8 Approximate Symmetry ................................... 45
Problem ..................................................... 46
References .................................................. 48
3 Chiral Perturbation Theory .................................. 49
3.1 Symmetries of Massless QCD ............................. 51
3.2 Spontaneous Symmetry Breaking .......................... 53
3.3 Transformation Rule .................................... 55
3.4 Effective Lagrangian ................................... 57
3.5 Power Counting ......................................... 59
3.6 Approximate Chiral Symmetry ............................ 62
3.7 Results from Approximate Symmetry ...................... 64
3.8 External Fields ........................................ 68
3.9 Fourth Order Effective Lagrangian ...................... 71
3.10 One-Loop Results (Pions Only) .......................... 75
3.11 Non-Goldstone Fields ................................... 80
3.12 Nucleon Current Correlation Function ................... 84
3.13 Meson Current Correlation Functions .................... 87
Problems .................................................... 91
References .................................................. 93
4 Thermal Propagators ......................................... 94
4.1 Time Path .............................................. 95
4.2 Scalar Propagator ...................................... 98
4.3 Dirac Propagator ...................................... 103
4.4 Time-Ordered Spectral Representation .................. 106
4.5 Retarded Spectral Representation ...................... 114
Problems ................................................... 115
References ................................................. 117
5 Thermal Perturbation Theory ................................ 118
5.1 Matrix Structure ...................................... 118
5.2 Diagonahsation ........................................ 123
5.3 One-Loop Self-Energy (Scalar Fields) .................. 126
5.4 One-Loop Self-Energy (General Fields) ................. 131
Problems ................................................... 134
References ................................................. 136
6 Thermal Parameters ......................................... 137
6.1 Quark Condensate at Finite Temperature ................ 138
6.2 Pion at Non-Zero Temperature .......................... 138
6.3 Nucleon at Finite Temperature ......................... 140
6.4 p at Finite Temperature ............................... 142
6.5 Nuclear Matter ........................................ 147
6.6 Comments .............................................. 151
Problem .................................................... 152
References ................................................. 153
7 Two-Loop Results ........................................... 154
7.1 Quark Condensate ...................................... 154
7.2 Pion Decay Rate ....................................... 159
7.3 Pion Mass and Coupling ................................ 163
Problems ................................................... 170
References ................................................. 172
8 Heavy Ion Collisions ....................................... 173
8.1 Dilepton Production ................................... 174
8.2 Analytic Structure .................................... 179
8.3 Evaluation ............................................ 182
8.4 Comments .............................................. 185
Problems ................................................... 185
References ................................................. 188
9 Non-Equilibrium Processes .................................. 189
9.1 Relativistic Hydrodynamics ............................ 190
9.2 Phenomenological Energy-Momentum Tensor ............... 192
9.3 Non-Equilibrium Statistical Theory .................... 194
9.4 Statistical Energy-Momentum Tensor .................... 197
9.5 Transport Coefficients ................................ 200
9.6 Evaluation ............................................ 203
Problem .................................................... 208
References ................................................. 210
Appendix A: General Fields .................................... 212
Appendix B: Global Symmetries ................................. 215
Appendix C: Exponential Operator .............................. 220
Appendix D: Propagator at Origin of Coordinates ............... 223
Appendix E: Reaction Rates in Vacuum and Medium ............... 227
Appendix F: Coupling Constants ................................ 233
Appendix G: Imaginary Time Method ............................. 238
Appendix H: Quark Condensate from Partition Function .......... 241
Appendix I: Quark Condensate from Density Expansion ........... 244
Index ......................................................... 246
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