Mathematical aspects of quantum field theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; United Kingdom
Cambridge University Press
2010
|
| Schriftenreihe: | Cambridge studies in advanced mathematics
127 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiii, 298 Seiten |
| ISBN: | 9780521115773 |
Internformat
MARC
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| 245 | 1 | 0 | |a Mathematical aspects of quantum field theory |c Edson de Farian: (Universidade de Sāu Paulo) ; Welington de Melo: (IMPA, Rio de Janeiro) |
| 264 | 1 | |a Cambridge ; United Kingdom |b Cambridge University Press |c 2010 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-020565078 | ||
Datensatz im Suchindex
| _version_ | 1804143258452885504 |
|---|---|
| adam_text | Contents
Foreword by Dennis Sullivan
page
ix
Preface
xi
1
Classical mechanics
1
1.1
Newtonian mechanics
1
1.2
Lagrangian mechanics
4
1.3
Hamiltonian mechanics
7
1.4
Poisson
brackets and Lie algebra structure of
observables
10
1.5
Symmetry and conservation laws: Noether s theorem
11
2
Quantum mechanics
14
2.1
The birth of quantum theory
14
2.2
The basic principles of quantum mechanics
16
2.3
Canonical quantization
21
2.4
From classical to quantum mechanics: the C* algebra
approach
24
2.5
The Weyl C* algebra
26
2.6
The quantum harmonic oscillator
29
2.7
Angular momentum quantization and spin
35
2.8
Path integral quantization
40
2.9
Deformation quantization
49
$
Relativity, the
Lorentz
group, and Dirac s equation
51
3.1
Relativity and the
Lorentz
group
51
3.2
Relaüvistic
kinematics
56
3.3
Relativistic dynamics
57
vi
Contents
3.4
The relativistic Lagrangian
58
3.5
Dirac s equation
60
Fiber bundles, connections, and representations
65
4.1
Fiber bundles and cocycles
65
4.2
Principal bundles
68
4.3
Connections
71
4.4
The gauge group
73
4.5
The Hodge
*
operator
75
4.6
Clifford algebras and spinor bundles
77
4.7
Representations
82
Classical field theory
93
5.1
Introduction
93
5.2
Electromagnetic field
94
5.3
Conservation laws in field theory
99
5.4
The Dirac field
103
5.5
Scalar fields
108
5.6
Yang-Mills fields
110
5.7
Gravitational fields
111
Quantization of classical fields
117
6.1
Quantization of free fields: general scheme
117
6.2
Axiomatic field theory
118
6.3
Quantization of bosonic free fields
122
6.4
Quantization of fermionic fields
128
6.5
Quantization of the free electromagnetic field
140
6.6
Wick rotations and axioms for Euclidean QFT
141
6.7
The CPT theorem
142
6.8
Scattering processes and LSZ reduction
144
Perturbative quantum field theory
153
7.1
Discretization of functional integrals
153
7.2
Gaussian measures and Wick s theorem
154
7.3
Discretization of Euclidean scalar fields
159
7.4
Perturbative quantum field theory
164
7.5
Perturbative Yang-Mills theory
182
Renormalization
192
8.1
Renormalization in perturbative QFT
192
8.2
Constructive field theory
201
Contents
vii
9 The
Standard
Model
204
9.1
Particles and fields
205
9.2
Particles and their quantum numbers
206
9.3
The quark model
207
9.4
Non-abelian gauge theories
209
9.5
Lagrangian formulation of the standard model
213
9.6
The intrinsic formulation of the Lagrangian
225
Appendix A
ι.:
Hilbert spaces and operators
232
A.I
Hubert spaces
232
A.2
Linear operators
233
A.3
Spectral theorem for compact operators
235
A.4
Spectral theorem for normal operators
237
A.5
Spectral theorem for unbounded operators
238
A.6
Functional calculus
245
A.7
Essential self-adjointness
247
A.8
A note on the spectrum
249
A.9
Stone s theorem
250
A.10
The Kato-Rellich theorem
253
Appendix
В
>:
C* algebras and spectral theory
258
B.I
Banach algebras
258
B.2
C* algebras
262
B.3
The spectral theorem
268
B.4
States and GNS representation
271
B.5
Representations and spectral resolutions
276
B.6
Algebraic quantum field theory
282
Bibliography
289
Index
293
|
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| discipline | Physik Mathematik |
| format | Book |
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| indexdate | 2024-07-09T22:44:48Z |
| institution | BVB |
| isbn | 9780521115773 |
| language | English |
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| spelling | Faria, Edson de (DE-588)136734782 aut Mathematical aspects of quantum field theory Edson de Farian: (Universidade de Sāu Paulo) ; Welington de Melo: (IMPA, Rio de Janeiro) Cambridge ; United Kingdom Cambridge University Press 2010 xiii, 298 Seiten txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 127 Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Quantum field theory--Mathematics. Quantenfeldtheorie (DE-588)4047984-5 s Mathematische Physik (DE-588)4037952-8 s DE-604 Mathematische Methode (DE-588)4155620-3 s Melo, Welington de 1946-2016 (DE-588)110394267 aut Erscheint auch als Online-Ausgabe 978-0-511-76053-2 Cambridge studies in advanced mathematics 127 (DE-604)BV000003678 127 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020565078&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Faria, Edson de Melo, Welington de 1946-2016 Mathematical aspects of quantum field theory Cambridge studies in advanced mathematics Quantenfeldtheorie (DE-588)4047984-5 gnd Mathematische Physik (DE-588)4037952-8 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4037952-8 (DE-588)4155620-3 |
| title | Mathematical aspects of quantum field theory |
| title_auth | Mathematical aspects of quantum field theory |
| title_exact_search | Mathematical aspects of quantum field theory |
| title_full | Mathematical aspects of quantum field theory Edson de Farian: (Universidade de Sāu Paulo) ; Welington de Melo: (IMPA, Rio de Janeiro) |
| title_fullStr | Mathematical aspects of quantum field theory Edson de Farian: (Universidade de Sāu Paulo) ; Welington de Melo: (IMPA, Rio de Janeiro) |
| title_full_unstemmed | Mathematical aspects of quantum field theory Edson de Farian: (Universidade de Sāu Paulo) ; Welington de Melo: (IMPA, Rio de Janeiro) |
| title_short | Mathematical aspects of quantum field theory |
| title_sort | mathematical aspects of quantum field theory |
| topic | Quantenfeldtheorie (DE-588)4047984-5 gnd Mathematische Physik (DE-588)4037952-8 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| topic_facet | Quantenfeldtheorie Mathematische Physik Mathematische Methode |
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