An introduction to non-perturbative foundations of quantum field theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford University Press
2013
|
| Ausgabe: | First edition |
| Schriftenreihe: | International series of monographs on physics
158 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xi, 257 Seiten |
| ISBN: | 9780199671571 |
Internformat
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| 245 | 1 | 0 | |a An introduction to non-perturbative foundations of quantum field theory |c Franco Strocchi |
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Datensatz im Suchindex
| _version_ | 1804150156531073024 |
|---|---|
| adam_text | Titel: An introduction to non-perturbative foundations of quantum field theory
Autor: Strocchi, Franco
Jahr: 2013
Contents
1 Relativistic quantum mechanics 1
1 Quantum mechanics and relativity 1
2 Relativistic Schrödinger wave mechanics 2
2.1 Relativistic Schrödinger equation 3
2.2 Klein-Gordon equation 4
2.3 Dirac equation 6
2.4 The general conflict between locality and energy positivity 8
3 Relativistic particle interactions and quantum mechanics 11
3.1 Problems of relativistic particle interactions 11
3.2 Field interactions and quantum mechanics 15
4 Free field equations and quantum mechanics 16
5 Particles as field quanta 20
6 Appendix: The Dirac equation 25
7 Appendix: Canonical field theory 29
2 Mathematical problems of the perturbative expansion 31
1 Dyson s perturbative expansion 31
2 Dyson argument against convergence 34
2.1 ip4 model in zero dimensions 35
2.2 (pA model in 0 + 1 dimensions 36
2.3 ipA model in 1+1 and 2+1 dimensions 38
3 Haag theorem; non-Fock representations 39
3.1 Quantum field interacting with a classical source 40
3.2 Bloch-Nordsieck model; the infrared problem 42
3.3 Yukawa model; non-perturbative renormalization 44
4 Ultraviolet singularities and canonical quantization 48
5 Problems of the interaction picture 52
6 Appendix: Locality and scattering 53
6.1 Locality and asymptotic states 53
6.2 Scattering by a long-range potential 57
6.3 Adiabatic switching 60
6.4 Asymptotic condition 61
7 Wick theorem and Feynman diagrams 63
7.1 Compton and electron-electron scattering;
electron-positron annihilation 67
3 Non-perturbative foundations of quantum field theory 69
1 Quantum mechanics and relativity 69
2 Properties of the vacuum correlation functions 72
x Contents
3 Quantum mechanics from correlation functions 75
4 General properties 78
4.1 Spectral condition and forward tube analyticity 78
4.2 Lorentz covariance and extended analyticity 79
4.3 Locality and permuted extended analyticity 81
4.4 Local structure of QFT 82
4.5 Quantization from spectral condition 83
4 General non-perturbative results and examples 85
1 Free evolution implies canonical quantization 85
2 Spin-statistics theorem 87
3 PCT theorem 91
4 Appendix: PCT theorem for spinor fields 93
5 Haag theorem 95
6 Ultraviolet singularities and non-canonical behavior 96
6.1 Schwinger terms in current commutators 96
6.2 Axial current anomaly and -kq - 27 decay 100
6.3 The derivative coupling model 103
5 Euclidean quantum field theory 107
1 The Schwinger functions 107
2 Euclidean invariance and symmetry 109
3 Reflection positivity 111
4 Cluster property 112
5 Laplace transform condition 113
6 From Euclidean to relativistic QFT 114
7 Examples 116
8 Functional integral representation 117
6 Non-perturbative S-matrix 121
1 LSZ asymptotic condition in QFT 121
2 Haag-Ruelle scattering theory (massive case) 123
2.1 One-body problem 123
2.2 Large time decay of smooth Solutions 125
2.3 Refined Cluster property 125
2.4 The asymptotic limit 127
2.5 The 5-matrix and asymptotic completeness 129
3 Buchholz scattering theory (massless particles) 129
3.1 Huyghens principle and locality 130
3.2 One-body problem 131
3.3 Asymptotic limit 132
4 Remarks on the infrared problem 134
7 Quantization of gauge field theories 140
1 Physical counterpart of gauge symmetry 140
2 Gauss law and locality 146
Contents xi
3 Local gauge quantization of QED 150
3.1 Weak Gauss law 150
3.2 Subsidiary condition and gauge invariance 152
3.3 Indefinite metric and Hilbert-Krein structure 154
3.4 Charged states 156
4 Local gauge quantization of the Yang-Mills theory 160
5 Gauss law and Charge superselection rule 166
5.1 Gauss charges in local gauges 167
5.2 Superselected charges and physical states 169
5.3 Electric Charge, current, and photon mass 169
6 Gauss law and Higgs mechanism 176
6.1 Local gauges 179
6.2 Coulomb gauge; a theorem on the Higgs phenomenon 180
6.3 Delocalization and gap in Coulomb Systems 184
7 Gauss law and infraparticles 186
8 Appendix: Quantization of the electromagnetic potential 191
8.1 Coulomb gauge 195
8.2 Feynman-Gupta-Bleuler quantization 197
8.3 Temporal gauge 202
8 Chiral symmetry breaking and vacuum structure in QCD 208
1 The (7(1) problem 208
2 Topology and chiral symmetry breaking in QCD 214
2.1 Temporal gauge and Gauss law 217
2.2 Topology of the gauge group 221
2.3 Fermions and chiral symmetry 225
2.4 Solution of the (7(1) problem 227
2.5 Topology and vacuum structure 228
2.6 Regulär temporal gauge 236
3 A lesson from the Schwinger model 240
Bibliography 245
Index 255
|
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| isbn | 9780199671571 |
| language | English |
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| spelling | Strocchi, Franco 1939- Verfasser (DE-588)172389348 aut An introduction to non-perturbative foundations of quantum field theory Franco Strocchi First edition Oxford Oxford University Press 2013 © 2013 xi, 257 Seiten txt rdacontent n rdamedia nc rdacarrier International series of monographs on physics 158 Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 s DE-604 Erscheint auch als Online-Ausgabe 978-0-19-165133-5 International series of monographs on physics 158 (DE-604)BV000106406 158 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025855595&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Strocchi, Franco 1939- An introduction to non-perturbative foundations of quantum field theory International series of monographs on physics Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4047984-5 |
| title | An introduction to non-perturbative foundations of quantum field theory |
| title_auth | An introduction to non-perturbative foundations of quantum field theory |
| title_exact_search | An introduction to non-perturbative foundations of quantum field theory |
| title_full | An introduction to non-perturbative foundations of quantum field theory Franco Strocchi |
| title_fullStr | An introduction to non-perturbative foundations of quantum field theory Franco Strocchi |
| title_full_unstemmed | An introduction to non-perturbative foundations of quantum field theory Franco Strocchi |
| title_short | An introduction to non-perturbative foundations of quantum field theory |
| title_sort | an introduction to non perturbative foundations of quantum field theory |
| topic | Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Quantenfeldtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025855595&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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