Effective field theories

목차 (Table of Contents)

• CONTENTS
• Preface = vii
• 1. Introduction = 1
• 1.1 Wherefore EFT? = 1
• 1.2 EFT vsMFT = 3
• 1.3 An example from Newton = 4
• 1.4 A theoremofWeinberg = 6
• 1.5 Organization of the book = 7
• 2. Symmetries = 9
• 2.1 Introduction = 9
• 2.2 Noether's Theorem = 9
• 2.3 Examples of Noether currents = 11
• 2.4 Gauged symmetries and Noether's procedure = 13
• 2.5 Broken symmetries and Goldstone's Theorem = 15
• 2.5.1 Nonrelativistic NG-bosons = 18
• 2.6 The BEHGHK Mechanism of Anderson = 20
• 2.6.1 A little history = 21
• 2.6.2 An example = 23
• 2.6.3 An interlude : superconductivity = 25
• 2.7 CCWZ construction of EFT = 27
• 2.8 Explicit breaking : spurion analysis = 30
• 2.9 Anomalous symmetries = 32
• 2.9.1 Anomalies in the path integral = 33
• 2.9.2 The chiral anomaly and its consequences = 35
• 2.9.3 't Hooft anomaly matching = 37
• 2.10 Notes for further reading = 38
• 3. Elementary Techniques = 41
• 3.1 Canonical (engineering) dimensions = 41
• 3.1.1 Dimensional analysis = 41
• 3.1.2 Example : hydrogen atom = 44
• 3.2 Dimensional transmutation = 46
• 3.3 Callan-Symanzik Equation = 49
• 3.4 The renormalization group = 53
• 3.4.1 Engineering dimensions of Г(n) = 53
• 3.4.2 Physics of the anomalous dimension = 54
• 3.5 Renormalizability and Effective Field Theory = 57
• 3.5.1 Dropping renormalizability = 57
• 3.5.2 Matching = 57
• 3.6 Subtraction schemes as part of EFT definition = 58
• 3.7 Decoupling. Appelquist-Carrazone theorem in various schemes = 60
• 3.8 Notes for further reading = 63
• 4. Effective Field Theories of TypeⅠ = 65
• 4.1 Introduction = 65
• 4.2 Real physics : Euler-Heisenberg Lagrangian = 70
• 4.3 Fermi Theory of Weak Interactions as an effective theory = 71
• 4.4 Fermi theory to one loop : △S＝2 processes in EFT = 73
• 4.4.1 Setting up the EFT approach = 74
• 4.4.2 A more detailed calculation = 76
• 4.5 QCD corrections in EFTs = 78
• 4.5.1 Matching at one loop in QCD = 79
• 4.5.2 Renormalization group improvement and EFTs = 83
• 4.5.3 Complete basis. Penguin operators = 85
• 4.6 Chiral perturbation theory = 88
• 4.6.1 Goldstone bosons and their properties = 90
• 4.6.2 Sources in chiral perturbation theory = 93
• 4.6.3 Applications : Gell-Mann-Okubo relation = 97
• 4.6.4 Power counting. Chiral loops and higher orders in χPT = 99
• 4.6.5 Naive dimensional analysis = 101
• 4.6.6 Baryons and chiral perturbation theory = 103
• 4.7 Notes for further reading = 104
• 5. Effective Field Theories of Type Ⅱ. Part A. = 107
• 5.1 Introduction = 107
• 5.2 Heavy Quark Effective Theory = 108
• 5.2.1 Quantum mechanics of heavy particles = 109
• 5.2.2 From quantum mechanics to field theory : HQET. Field redefinitions = 111
• 5.2.3 Spin symmetry and its consequences = 115
• 5.2.4 More symmetry : reparameterization invariance = 117
• 5.2.5 HQET Green's functions. Radiative corrections = 118
• 5.2.6 External currents and external states = 122
• 5.3 Different degrees of freedom : heavy mesons = 130
• 5.3.1 Heavy meson states. Tensor formalism = 130
• 5.3.2 Leading-order Lagrangian = 133
• 5.3.3 Subleading Lagrangians = 134
• 5.3.4 Calculations with HHχPT = 135
• 5.4 Light baryons in heavy particle formalism = 139
• 5.4.1 Leading-order Lagrangian = 139
• 5.5 Notes for further reading = 142
• 6. Effective Field Theories of Type-Ⅱ. Part B. = 145
• 6.1 Introduction. Non-relativistic QED and QCD = 145
• 6.2 NRQCD Lagrangian at the scale mQ = 147
• 6.3 Going down : non-perturbative scales mQv and mQv² = 151
• 6.3.1 Electromagnetic decays of the ηc = 155
• 6.3.2 Inclusive decays of the ηc into light hadrons = 156
• 6.3.3 Inclusive decays of the χcJ into light hadrons = 158
• 6.4 Going down : perturbative scales mQv and mQv². pNRQCD = 160
• 6.4.1 Example : heavy quarkonium potential = 161
• 6.5 Different degrees of freedom : hadronic molecules = 163
• 6.6 Notes for further reading = 168
• 7. Effective Field Theories of Type-Ⅲ. Fast Particles in Effective Theories = 171
• 7.1 Infrared divergences = 171
• 7.2 Soft-Collinear Effective Theory = 174
• 7.2.1 Quantum mechanics of fast particles = 174
• 7.2.2 SCET power counting = 175
• 7.2.3 SCET action = 178
• 7.3 Symmetries of SCET = 182
• 7.3.1 Gauge invariance = 182
• 7.3.2 Reparametrization invariance = 184
• 7.4 Examples = 185
• 7.4.1 B → Xsγ = 185
• 7.4.2 B → Dπ = 188
• 7.4.3 Deep Inelastic Scattering = 191
• 7.4.4 Jet production = 197
• 7.5 Notes for further reading = 199
• 8. Standard Model as an Effective Field Theory = 203
• 8.1 Introduction = 203
• 8.2 Standard model as the leading term in the EFT expansion = 205
• 8.2.1 Dimension-5 operators : fermion number violation = 206
• 8.2.2 Dimension-6 operators : parameterizing new physics = 208
• 8.2.3 Experimental tests and observables = 209
• 8.3 BSM particles in EFT = 211
• 8.3.1 Dark matter at colliders : effective operators = 212
• 8.3.2 Mono-Higgs signatures of dark matter at LHC = 213
• 8.4 Notes for further reading = 217
• 9. Effective Field Theories of Gravity = 219
• 9.1 Introduction = 219
• 9.2 Review of general relativity = 221
• 9.2.1 Geodesics and affine connection = 221
• 9.2.2 General relativity and the weak field limit = 222
• 9.2.3 Gravity sources : energy-momentum tensor = 226
• 9.3 Building an effective field theory = 227
• 9.3.1 Quantization. Feynman rules = 228
• 9.3.2 Quantum EFT for gravity = 231
• 9.3.3 Newtonian potential = 233
• 9.3.4 Postscript = 234
• 9.4 Classical EFT : NRGR = 235
• 9.4.1 Setting up the problem = 236
• 9.4.2 Gravitionmodes = 238
• 9.4.3 Feynman rules = 241
• 9.4.4 Gravitational radiation = 242
• 9.4.5 Renormalization = 245
• 9.5 Notes for further reading = 247
• 10. Outlook = 249
• 10.1 Supersymmetry = 249
• 10.2 Extra dimensions = 250
• 10.3 Technicolor and compositeness = 251
• 10.4 High-Tc superconductivity = 252
• Appendix A : Review of Group Theory = 253
• A.1 General definitions = 253
• A.2 Continuous groups = 255
• A.3 Representation theory of Lie groups = 258
• A.4 Young Tableaux for SU(N) = 262
• A.5 Group theory coefficients = 266
• A.6 Notes for further reading = 267
• Appendix B : Short Review of QED and QCD = 269
• B.1 Quantum electrodynamics = 269
• B.2 Quantum chromodynamics = 270
• B.2.1 QCD Lagrangian and Feynman rules = 271
• B.2.2 Symmetries of the QCD Lagrangian = 277
• Appendix C : Useful Features of Dimensional Regularization = 279
• C.1 Overview of dimensional regularization = 279
• C.2 Useful formulas = 280
• C.3 Dimensional regularization vs other schemes = 282
• C.4 Advanced features : scaleless integrals = 283
• C.5 Advanced features : integration by parts = 285
• C.6 Advanced features : method of regions = 287
• Bibliography = 291
• Index = 301