Quantum mechanics and quantum field theory: a mathematical primer
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2011
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Cover image Inhaltsverzeichnis |
| Physical Description: | XI, 226 S. |
| ISBN: | 9781107005099 |
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Record in the Search Index
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| adam_text | Titel: Quantum mechanics and quantum field theory
Autor: Dimock, Jonathan
Jahr: 2011
Preface page xi
Introduction 1
Part I Non-relativistic 3
1 Mathematical prelude 5
1.1 Bounded operators 5
1.2 Unbounded operators 11
1.3 Self-adjoint operators 14
1.4 Compact operators 22
2 Classical mechanics 28
2.1 Hamiltonian mechanics 28
2.2 Examples 29
2.3 Canonical transformations 31
2.4 Symmetries 34
3 Quantum mechanics 38
3.1 Principles of quantum mechanics 38
3.2 Canonical quantization 41
3.3 Symmetries 43
3.4 Perspectives and problems 45
4 Single particle 47
4.1 Free particle 47
4.2 Particle in a potential 48
4.3 Spectrum 51
4.4 The harmonic oscillator 53
Contents
4.5 Scattering
4.6 Spin
5 Many particles
5.1 Two particles
5.2 Identical particles
5.3 «-particles
5.4 Fock space
6 Statistical mechanics
6.1 Mixed states
6.2 Equilibrium states
6.3 Free boson gas
6.4 Free fermion gas
6.5 Interacting bosons
6.6 Further developments
Part II Relativistic
55
58
63
63
66
67
70
78
78
79
83
86
88
90
93
7 Relativity
7.1 Principles of relativity
7.2 Minkowski space
7.3 Classical free fields
7.4 Interacting classical fields
7.5 Fundamental solutions
8 Scalar particles and fields
8.1 Scalar particles
8.2 Scalar fields
8.3 Charged scalar field
9 Electrons and photons
9.1 Spinors
9.2 Electrons
9.3 Dirac fields
9.4 Photons
9.5 Electromagnetic field
10 Field theory on a manifold
10.1 Lorentzian manifolds
95
95
96
103
107
111
114
114
118
126
130
130
132
139
144
148
152
152
Contents
10.2 Classical fields on a manifold 154
10.3 Quantum fields on a manifold 155
Partili Probabilistic methods 159
11 Path integrals 161
11.1 Probability 161
11.2 Gaussian processes 163
11.3 Brownian motion 165
11.4 The Feynman-Kac formula 168
11.5 Oscillator process 169
11.6 Application: ground states 171
12 Fields as random variables 174
12.1 More on Gaussian processes 174
12.2 The Schrödinger representation 181
12.3 Path integrals - free fields 184
12.4 Vacuum correlation functions 187
12.5 Thermal correlation functions 189
13 A nonlinear field theory 192
13.1 The model 192
13.2 Regularization 193
13.3 Infinite volume 197
13.4 Path integrals - interacting fields 201
13.5 A reformulation 204
Appendix A Normed spaces 208
Appendix ? Tensor product 211
AppendixC Distributions 215
References 219
Index 222
|
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| discipline | Physik |
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| isbn | 9781107005099 |
| language | English |
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| physical | XI, 226 S. |
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| spelling | Dimock, Jonathan 1945- Verfasser (DE-588)14399574X aut Quantum mechanics and quantum field theory a mathematical primer Jonathan Dimock 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2011 XI, 226 S. txt rdacontent n rdamedia nc rdacarrier Mathematik Quantentheorie Quantum theory Mathematics SCIENCE / Mathematical Physics bisacsh Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s Quantenfeldtheorie (DE-588)4047984-5 s DE-604 http://assets.cambridge.org/97811070/05099/cover/9781107005099.jpg Cover image HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020871315&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dimock, Jonathan 1945- Quantum mechanics and quantum field theory a mathematical primer Mathematik Quantentheorie Quantum theory Mathematics SCIENCE / Mathematical Physics bisacsh Quantenmechanik (DE-588)4047989-4 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4047984-5 |
| title | Quantum mechanics and quantum field theory a mathematical primer |
| title_auth | Quantum mechanics and quantum field theory a mathematical primer |
| title_exact_search | Quantum mechanics and quantum field theory a mathematical primer |
| title_full | Quantum mechanics and quantum field theory a mathematical primer Jonathan Dimock |
| title_fullStr | Quantum mechanics and quantum field theory a mathematical primer Jonathan Dimock |
| title_full_unstemmed | Quantum mechanics and quantum field theory a mathematical primer Jonathan Dimock |
| title_short | Quantum mechanics and quantum field theory |
| title_sort | quantum mechanics and quantum field theory a mathematical primer |
| title_sub | a mathematical primer |
| topic | Mathematik Quantentheorie Quantum theory Mathematics SCIENCE / Mathematical Physics bisacsh Quantenmechanik (DE-588)4047989-4 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Mathematik Quantentheorie Quantum theory Mathematics SCIENCE / Mathematical Physics Quantenmechanik Quantenfeldtheorie |
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