Advanced Field Theory

Cover......Page 1
Title......Page 2
Title page......Page 3
Copyright page......Page 4
Contents......Page 5
Preface......Page 11
1.1 Micro, Macro, and Thermal......Page 13
1.2 Classical Physics for Particles and Fields......Page 15
1.3 Quantum Mechanics and Quantum Field Theory......Page 20
1.4 The c-q Transmutation Condition......Page 24
1.5 Matter and the Vacuum......Page 25
1.6 References......Page 26
2.1 Number Representation......Page 27
2.2.1 Coherent States......Page 28
2.2.2 Squeezed States......Page 31
2.2.3 Two-Mode Squeezed States......Page 33
2.2.4 An Equivalence Theorem......Page 35
2.3.1 Thermal-Like Noise in the Two-Mode State......Page 36
2.3.2 Correlation through the Vacuum......Page 38
2.4.1 Bosonic System......Page 40
2.4.2 Thermal Vacuum for Fermionic Oscillators......Page 42
2.4.3 Non-Trivial Parameters in Vacua......Page 44
2.5 TFD Mechanism for Noise Creation......Page 45
2.6 TFD Mechanism and Black Hole......Page 46
2.7 Phase and Time Operators in TFD......Page 47
2.8 References......Page 49
3.1.1 Infrared Catastrophe of Bremsstrahlung......Page 51
3.1.2 Vacuum Polarization......Page 52
3.2 Many Vacua......Page 54
3.3 Anomalous Operators......Page 57
3.4.1 Bosonic Systems......Page 58
3.4.2 Fermionic Systems......Page 59
3.5 References......Page 61
4.2 Countably Infinite Degrees of Freedom......Page 62
4.4 Quasi-Particles and Dynamical Map......Page 64
4.5 Time-Independent Global Operators......Page 67
4.6.1 Quasi-Particle Free Hamiltonian......Page 69
4.6.3 Asymptotic Fields and Quasi-Particles......Page 71
4.6.4 Many Choices for Incoming Particles......Page 73
4.6.5 Renormalization......Page 74
4.7 References......Page 75
5.1.1 A Physical Picture......Page 76
5.1.2 A Mathematical Picture......Page 77
5.1.3 Symmetry Rearrangement......Page 79
5.1.4 Boson Transformation......Page 80
5.1.6 Generators and the Nöther Current......Page 81
5.1.7 The Ward-Takahashi Relations......Page 82
5.1.8 $\\theta$-Selection......Page 83
5.1.9 Summary of this Section......Page 85
5.2.3 The Nöther Current and the Generator......Page 86
5.2.5 The Order Parameter and $\\theta$-Selection......Page 87
5.2.7 A Fluctuation Effect......Page 88
5.2.8 A Strategy for Computational Analysis......Page 90
5.3.1 Introduction......Page 91
5.3.2 The BCS Model......Page 92
5.3.4 Phase Symmetry Rearrangement......Page 93
5.3.6 The Nambu-Goldestone Field......Page 94
5.3.7 Are NG-Bosons Entirely Eliminated?......Page 95
5.3.8 Order Parameter and $\\theta$-Selection......Page 96
5.3.9 A Fluctuation Effect......Page 97
5.3.10 Gauge Invariance......Page 98
5.3.11 A Strategy in Computational Analysis......Page 99
5.4.1 Spontaneously Broken Spin Symmetry......Page 100
5.4.2 Symmetry Rearrangement......Page 103
5.4.3 Low Energy Theorem II......Page 104
5.5 c-q Transmutation and Crystal Phonon......Page 105
5.6 The Spontaneous Creation of Mass......Page 107
5.7 References......Page 109
6.1.2 Planck\'s Constant......Page 111
6.1.3 Boson Transformation......Page 112
6.1.4 Induced Potential and Zero-Energy Mode......Page 114
6.1.5 Quantum Mechanical Operators......Page 117
6.1.6 Asymptotic Condition for Free Particles......Page 119
6.1.8 Quasi-Static Objects and Singularities......Page 121
6.1.9 Many Objects and Many Conservation Laws......Page 123
6.2.1 (1 + 1)-Dimensional objects......Page 124
6.2.2 Three-Dimensional Models......Page 127
6.2.3 Macroscopic Objects with a Fermion......Page 128
6.3.1 Stable Solitons......Page 130
6.3.2 Unstable Solitons......Page 132
6.4.1 Path-Dependent Topology......Page 133
6.4.2 Superfluid Vortices......Page 134
6.4.3 Superconducting Vortices......Page 136
6.4.4 A General Formalism......Page 138
6.4.5 Defects and the Original Symmetry......Page 140
6.5.1 Two Views......Page 141
6.5.2 Condensed Matter Physics......Page 142
6.5.3 Nuclear Physics and High Energy Physics......Page 143
6.6 Biological Order......Page 144
6.7 References......Page 146
7.1 Introduction......Page 149
7.2.1 Thermal Doublets and Hamiltonian......Page 152
7.2.2 The Tilde Conjugation Rules......Page 156
7.2.3 Non-Hermitian Representation of TFD......Page 159
7.2.4 Spontaneous breakdown of $G$-symmetry......Page 162
7.2.5 The Thermal State Condition......Page 163
7.2.6 One-Body Propagators in TFD......Page 165
7.3 The General Structure of TFD......Page 171
7.4 Thermal Observable......Page 174
7.5.1 The Interaction Representation......Page 176
7.5.2 Vacuum Stability and Temperature States......Page 179
7.6 References......Page 182
8.1.1 The Choices for $\\alpha$......Page 184
8.1.2 Product Rules for Loops......Page 185
8.1.3 The Spectral Representation......Page 187
8.1.5 The Kubo-Martin-Schwinger Condition......Page 194
8.1.6 Free Energy......Page 195
8.1.8 The Thermal Breakdown of Symmetries......Page 196
8.1.9 Thermal Quantum Field Theories......Page 197
8.2.2 Preparation......Page 204
8.2.3 One-Body Propagator......Page 206
8.3 References......Page 209
9.1.1 A Motivation......Page 215
9.2.1 Time-Dependent Bogoliubov Transformations......Page 216
9.2.2 The Unperturbed One-Body Propagator......Page 220
9.2.3 The Corrected Particle Number......Page 221
9.2.4 Heisenberg Number and Corrected Number......Page 225
9.2.5 Product Rules......Page 226
9.2.6 The Kinetic Equation......Page 230
9.3.1 The Bogoliubov Transformations......Page 235
9.3.2 The Unperturbed Hamiltonian......Page 237
9.3.3 Time-Space Dependent TFD for Fields......Page 238
9.3.4 The Unperturbed One-Body Propagator......Page 239
9.5 Comments......Page 240
9.6 References......Page 242
Index......Page 244