دانلود کتاب The Pinch Technique and its Applications to Non-Abelian Gauge Theories (Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology)

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Cover......Page 1
Half-title......Page 3
Series-title......Page 4
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Introduction: Why the pinch technique?......Page 13
A quick outline of the book......Page 15
Some uses of the pinch technique......Page 16
Constructing pinch technique Green\'s functions and equations......Page 17
1.1 A brief history......Page 21
1.2 Notation and conventions......Page 23
1.3 The basic one-loop pinch technique......Page 26
1.3.1 Origin of the longitudinal momenta......Page 27
1.3.2 The basic pinch operation......Page 30
1.3.3 The pinch technique gluon self-energy at one loop......Page 34
1.4.1 Process independence......Page 37
1.4.2 Intrinsic pinch technique......Page 39
1.5.1 The one-loop pinch technique quark-gluon vertex and its Ward identity......Page 40
1.5.2 The one-loop, three-gluon vertex and its Ward identity......Page 43
1.5.3 The four-gluon vertex......Page 50
1.6 The pinch technique in the light-cone gauge......Page 51
1.7 The absorptive pinch technique construction......Page 54
1.7.1 The strong version of the optical theorem......Page 56
1.7.2 The fundamental s-t cancellation......Page 58
1.8 Positivity and the pinch technique gluon propagator......Page 62
References......Page 63
2.1 The pinch technique and the operator product expansion: Running mass and condensates......Page 65
2.2.1 General remarks......Page 67
2.2.2 Dynamical gauge-boson mass generation in QCD......Page 69
2.2.3 The need for dynamical mass in d=2+1 QCD......Page 70
2.2.4 What do vertices and propagators look like when dynamical mass is generated?......Page 71
2.2.5 Mass generation through Higgs–Kibble–Goldstone fields......Page 75
2.3 The pinch technique today: Background-field Feynman gauge......Page 82
2.3.1 The effective action......Page 83
2.3.2 The background-field method for gauge fields......Page 86
2.3.3 Pinch technique and background Feynman gauge correspondence......Page 89
2.3.4 The generalized pinch technique......Page 91
2.4 What to expect beyond one loop......Page 92
References......Page 93
3.1 The s-t cancellation to all orders......Page 95
3.2 Quark-gluon vertex and gluon propagator to all orders......Page 99
References......Page 105
4 The pinch technique in the Batalin–Vilkovisky framework......Page 106
4.1.2 The Batalin–Vilkovisky formalism......Page 108
4.2.1 Slavnov–Taylor identities......Page 113
4.2.2 Background-quantum identities......Page 115
4.2.3 Closed expressions for auxiliary functions......Page 117
4.2.4 A special case: The (background) Landau gauge......Page 119
4.3 Pinching in the Batalin–Vilkovisky framework......Page 120
References......Page 122
5 The gauge technique......Page 124
5.1.1 Scalar QED......Page 125
5.1.2 Fermionic QED......Page 127
5.2 Massless longitudinal poles......Page 128
5.3 The gauge technique for NAGTs......Page 129
5.3.1 The gauge technique in the light-cone gauge......Page 131
References......Page 133
6 Schwinger–Dyson equations in the pinch technique framework......Page 134
6.1 Lattice studies of gluon mass generation......Page 135
6.2 The need for a gauge-invariant truncation scheme for the Schwinger–Dyson equations of NAGTs......Page 137
6.3 The pinch technique algorithm for Schwinger–Dyson equations......Page 139
6.4 Pinch technique Green\'s functions from Schwinger–Dyson equations......Page 140
6.4.1 First step:…......Page 141
6.4.2 Second step:…......Page 143
6.4.3 Third step:…......Page 145
6.4.4 The final rearrangement and the new Schwinger–Dyson equation......Page 146
6.4.5 Truncation of the pinch technique Schwinger–Dyson equation......Page 150
6.5 Solutions of the pinch technique Schwinger–Dyson equations and comparison with lattice data......Page 151
6.6.1 The prototype: The QED effective charge......Page 154
6.6.2 The QCD effective charge......Page 155
References......Page 161
7.2 Introduction......Page 164
7.2.1 Condensates and solitons......Page 165
7.2.2 What does confinement really mean?......Page 167
7.3 The quantum solitons......Page 170
7.4.1 The standard Abelian center vortex......Page 172
7.4.2 The general center vortex......Page 175
7.4.3 The Q-matrices and the center-vortex homotopy......Page 176
7.4.4 Confinement......Page 179
7.4.5 Screening......Page 183
7.4.6 Hybrids......Page 184
References......Page 185
8.1.1 Junctions......Page 187
8.1.2 Nexuses, magnetic charge, and topological charge......Page 188
8.2.1 The SU(2) nexus......Page 190
8.2.3 Nexus magnetic charge......Page 192
8.2.4 Topological charge as an intersection number for nonorientable vortex surfaces......Page 194
8.3 The QCD sphaleron......Page 201
8.3.1 The QCD sphaleron as a d=3 object......Page 203
8.3.2 Sphalerons in four-dimensional Minkowski space......Page 204
8.4 Chiral symmetry breakdown, nexuses, and fractional topological charge......Page 206
References......Page 208
9.1 Introduction......Page 210
9.3 The exact form of the zero-momentum effective action......Page 213
9.3.1 The effective action and the pinch technique......Page 215
9.4.1 Early pinch technique work......Page 217
9.4.2 One-loop gap equations and lattice simulations......Page 218
9.5 The functional Schrodinger equation......Page 221
9.5.1 The gauge technique and the FSE......Page 223
9.5.2 The proposed infrared-effective action......Page 225
9.6 Dynamical gluon mass versus the Chern–Simons mass: Two phases......Page 229
9.6.1 The nonperturbative phase uncovered by the pinch technique......Page 231
9.6.2 YMCS solitons......Page 234
9.7 Compactness and the Chern–Simons number of YMCS solitons......Page 236
9.7.1 Sphalerons, knots, and compactness......Page 240
References......Page 243
10 The pinch technique for electroweak theory......Page 246
10.1 General considerations......Page 247
10.2 The case of massless fermions......Page 249
10.2.1 The unitary gauge......Page 256
10.2.2 Absorptive construction in the electroweak sector......Page 257
10.2.3 Background field method away from xi Q=1: physical versus unphysical thresholds......Page 260
10.3 Nonconserved currents and Ward identities......Page 262
10.4 The all-order construction......Page 266
References......Page 268
11.2 Non-Abelian effective charges......Page 270
11.2.1 Electroweak effective charges......Page 271
11.2.2 Relation to physical cross sections......Page 272
11.3 Physical renormalization schemes versus MS......Page 275
11.4 Gauge-independent off-shell form factors......Page 276
11.4.1 Neutrino charge radius......Page 279
11.5 Resummation formalism for resonant transition amplitudes......Page 283
11.5.1 An example......Page 285
11.6 The pinch technique at finite temperature......Page 290
11.7 Basic principles of thermal field theory......Page 291
11.7.1 The pinch technique in the zero-Matsubara-frequency sector......Page 292
11.7.2 Developments in the full thermal field theory......Page 294
11.8 Hints of supersymmetry in the pinch technique Green\'s functions......Page 296
References......Page 298
A.3 BFM sources......Page 301
Index......Page 305