Quantum field theory: a tourist guide for mathematicians
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2008]
|
| Series: | Mathematical surveys and monographs
Volume 149 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xi, 325 Seiten Illustrationen, Diagramme |
| ISBN: | 0821847058 9780821847053 |
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MARC
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Record in the Search Index
| _version_ | 1804138041653067776 |
|---|---|
| adam_text | Contents
Preface
vu
Chapter
1.
Prologue
1
1.1.
Linguistic
prologue: notation
and terminology
1
1.2.
Physical
prologue: dimensions,
units,
constants,
and particles
5
1.3.
Mathematical
prologue:
some Lie groups and Lie algebras
8
Chapter
2.
Review of Pre-quantum Physics
13
2.1.
Mechanics according to Newton and Hamilton
13
2.2.
Mechanics according to
Lagrange 18
2.3.
Special relativity
22
2.4.
Electromagnetism
25
Chapter
3.
Basic Quantum Mechanics
33
3.1.
The mathematical framework
33
3.2.
Quantization
42
3.3.
Uncertainty inequalities
51
3.4.
The harmonic oscillator
53
3.5.
Angular momentum and spin
56
3.6.
The Coulomb potential
60
Chapter
4.
Relativistic Quantum Mechanics
65
4.1.
The Klein-Gordon and Dirac equations
66
4.2.
Invariance
and covariance properties of the Dirac equation
70
4.3.
Consequences of the Dirac equation
74
4.4.
Single-particle state spaces
83
4.5.
Multiparticle state spaces
89
Chapter
5.
Pree
Quantum Fields
97
5.1.
Scalar fields
97
5.2.
The rigorous construction
105
5.3.
Lagrangians and Hamiltonians
107
5.4.
Spinor and vector fields
112
5.5.
The Wightman axioms
119
Chapter
6.
Quantum Fields with Interactions
123
6.1.
Perturbation theory
123
6.2.
A toy model for electrons in an atom
128
6.3.
The scattering matrix
136
6.4.
Evaluation of the S-matrix: first steps
143
6.5.
Propagators
147
vi
CONTENTS
6.6.
Feynman
diagrams
154
6.7.
Feynman
diagrams in momentum space
162
6.8.
Cross sections and decay rates
167
6.9.
QED, the Coulomb potential, and the Yukawa potential
172
6.10.
Compton scattering
177
6.11.
The Gell-Mann-Low and LSZ formulas
180
Chapter
7.
Renormalization
191
7.1.
Introduction
192
7.2.
Power counting
196
7.3.
Evaluation and regularization of Feynman diagrams
200
7.4.
A one-loop calculation in scalar field theory
206
7.5.
Renormalized perturbation theory
211
7.6.
Dressing the propagator
214
7.7.
The Ward identities
219
7.8.
Renormalization in QED: general structure
224
7.9.
One-loop QED: the electron propagator
234
7.10.
One-loop QED: the photon propagator and vacuum polarization
237
7.11.
One-loop QED: the vertex function and magnetic moments
244
7.12.
Higher-order renormalization
251
Chapter
8.
Functional Integrals
257
8.1.
Functional integrals and quantum mechanics
257
8.2.
Expectations, functional derivatives, and generating functionals
265
8.3.
Functional integrals and Boson fields
271
8.4.
Functional integrals and Fermion fields
278
8.5.
Afterword: Gaussian processes
287
Chapter
9.
Gauge Field Theories
291
9.1.
Local symmetries and gauge fields
291
9.2.
A glimpse at quantum chromodynamics
296
9.3.
Broken symmetries
299
9.4.
The electroweak theory
303
Bibliography
317
Index
323
|
| adam_txt |
Contents
Preface
vu
Chapter
1.
Prologue
1
1.1.
Linguistic
prologue: notation
and terminology
1
1.2.
Physical
prologue: dimensions,
units,
constants,
and particles
5
1.3.
Mathematical
prologue:
some Lie groups and Lie algebras
8
Chapter
2.
Review of Pre-quantum Physics
13
2.1.
Mechanics according to Newton and Hamilton
13
2.2.
Mechanics according to
Lagrange 18
2.3.
Special relativity
22
2.4.
Electromagnetism
25
Chapter
3.
Basic Quantum Mechanics
33
3.1.
The mathematical framework
33
3.2.
Quantization
42
3.3.
Uncertainty inequalities
51
3.4.
The harmonic oscillator
53
3.5.
Angular momentum and spin
56
3.6.
The Coulomb potential
60
Chapter
4.
Relativistic Quantum Mechanics
65
4.1.
The Klein-Gordon and Dirac equations
66
4.2.
Invariance
and covariance properties of the Dirac equation
70
4.3.
Consequences of the Dirac equation
74
4.4.
Single-particle state spaces
83
4.5.
Multiparticle state spaces
89
Chapter
5.
Pree
Quantum Fields
97
5.1.
Scalar fields
97
5.2.
The rigorous construction
105
5.3.
Lagrangians and Hamiltonians
107
5.4.
Spinor and vector fields
112
5.5.
The Wightman axioms
119
Chapter
6.
Quantum Fields with Interactions
123
6.1.
Perturbation theory
123
6.2.
A toy model for electrons in an atom
128
6.3.
The scattering matrix
136
6.4.
Evaluation of the S-matrix: first steps
143
6.5.
Propagators
147
vi
CONTENTS
6.6.
Feynman
diagrams
154
6.7.
Feynman
diagrams in momentum space
162
6.8.
Cross sections and decay rates
167
6.9.
QED, the Coulomb potential, and the Yukawa potential
172
6.10.
Compton scattering
177
6.11.
The Gell-Mann-Low and LSZ formulas
180
Chapter
7.
Renormalization
191
7.1.
Introduction
192
7.2.
Power counting
196
7.3.
Evaluation and regularization of Feynman diagrams
200
7.4.
A one-loop calculation in scalar field theory
206
7.5.
Renormalized perturbation theory
211
7.6.
Dressing the propagator
214
7.7.
The Ward identities
219
7.8.
Renormalization in QED: general structure
224
7.9.
One-loop QED: the electron propagator
234
7.10.
One-loop QED: the photon propagator and vacuum polarization
237
7.11.
One-loop QED: the vertex function and magnetic moments
244
7.12.
Higher-order renormalization
251
Chapter
8.
Functional Integrals
257
8.1.
Functional integrals and quantum mechanics
257
8.2.
Expectations, functional derivatives, and generating functionals
265
8.3.
Functional integrals and Boson fields
271
8.4.
Functional integrals and Fermion fields
278
8.5.
Afterword: Gaussian processes
287
Chapter
9.
Gauge Field Theories
291
9.1.
Local symmetries and gauge fields
291
9.2.
A glimpse at quantum chromodynamics
296
9.3.
Broken symmetries
299
9.4.
The electroweak theory
303
Bibliography
317
Index
323 |
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| institution | BVB |
| isbn | 0821847058 9780821847053 |
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| spelling | Folland, Gerald B. 1947- Verfasser (DE-588)137062486 aut Quantum field theory a tourist guide for mathematicians Gerald B. Folland Providence, Rhode Island American Mathematical Society [2008] © 2008 xi, 325 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 149 Kwantumveldentheorie gtt Théorie quantique des champs - Mathématique Électrodynamique quantique - Mathématiques Mathematik Quantum electrodynamics Mathematics Quantum field theory Mathematics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Quantenfeldtheorie (DE-588)4047984-5 s Mathematische Physik (DE-588)4037952-8 s DE-604 Mathematical surveys and monographs Volume 149 (DE-604)BV000018014 149 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016754833&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Folland, Gerald B. 1947- Quantum field theory a tourist guide for mathematicians Mathematical surveys and monographs Kwantumveldentheorie gtt Théorie quantique des champs - Mathématique Électrodynamique quantique - Mathématiques Mathematik Quantum electrodynamics Mathematics Quantum field theory Mathematics Mathematische Physik (DE-588)4037952-8 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4047984-5 (DE-588)1071861417 |
| title | Quantum field theory a tourist guide for mathematicians |
| title_auth | Quantum field theory a tourist guide for mathematicians |
| title_exact_search | Quantum field theory a tourist guide for mathematicians |
| title_exact_search_txtP | Quantum field theory a tourist guide for mathematicians |
| title_full | Quantum field theory a tourist guide for mathematicians Gerald B. Folland |
| title_fullStr | Quantum field theory a tourist guide for mathematicians Gerald B. Folland |
| title_full_unstemmed | Quantum field theory a tourist guide for mathematicians Gerald B. Folland |
| title_short | Quantum field theory |
| title_sort | quantum field theory a tourist guide for mathematicians |
| title_sub | a tourist guide for mathematicians |
| topic | Kwantumveldentheorie gtt Théorie quantique des champs - Mathématique Électrodynamique quantique - Mathématiques Mathematik Quantum electrodynamics Mathematics Quantum field theory Mathematics Mathematische Physik (DE-588)4037952-8 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Kwantumveldentheorie Théorie quantique des champs - Mathématique Électrodynamique quantique - Mathématiques Mathematik Quantum electrodynamics Mathematics Quantum field theory Mathematics Mathematische Physik Quantenfeldtheorie Konferenzschrift |
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