The Schwinger action principle and effective action:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge monographs on mathematical physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XI, 495 S. graph. Darst. |
| ISBN: | 9780521876766 |
Internformat
MARC
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| 100 | 1 | |a Toms, David J. |d 1953- |e Verfasser |0 (DE-588)139157107 |4 aut | |
| 245 | 1 | 0 | |a The Schwinger action principle and effective action |c David J. Toms |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2007 | |
| 300 | |a XI, 495 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Cambridge monographs on mathematical physics | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Schwinger action principle | |
| 650 | 4 | |a Quantum theory | |
| 650 | 4 | |a Mathematical physics | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016174002 | ||
Datensatz im Suchindex
| _version_ | 1804137220795269120 |
|---|---|
| adam_text | Contents
Preface
page
χ
1
Action principle in classical mechanics
1
1.1
Euler-Lagrange equations
1
1.2
Hamilton s principle
5
1.3
Hamilton s equations
8
1.4
Canonical transformations
12
1.5
Conservation laws and symmetries
22
Notes
38
2
Action principle in classical field theory
40
2.1
Continuous systems
40
2.2
Lagrangian and Hamiltonian formulation for
continuous systems
43
2.3
Some examples
48
2.4
Functional differentiation and
Poisson
brackets for
field theory
54
2.5
Noether s theorem
60
2.6
The stress-energy-momentum tensor
66
2.7
Gauge
invariance
75
2.8
Fields of general spin
83
2.9
The Dirac equation
88
Notes
99
3
Action principle in quantum theory
100
3.1
States and
observables
100
3.2 Schwinger
action principle 111
3.3
Equations of motion and canonical commutation relations
113
3.4
Position and momentum eigenstates
120
3.5
Simple harmonic oscillator
124
3.6
Real scalar field
132
VII
viii Contents
3.7
Complex scalar
field
140
3.8 Schrödinger
field
144
3.9
Dirac field
151
3.10
Electromagnetic field
157
Notes
168
4
The effective action
169
4.1
Introduction
169
4.2
Free scalar field in Minkowski spacetime
174
4.3 Casimir
effect
178
4.4
Constant gauge field background
181
4.5
Constant magnetic field
186
4.6
Self-interacting scalar field
196
4.7
Local
Casimir
effect
203
Notes
207
5
Quantum statistical mechanics
208
5.1
Introduction
208
5.2
Simple harmonic oscillator
213
5.3
Real scalar field
217
5.4
Charged scalar field
221
5.5
Non-relativistic field
228
5.6
Dirac field
234
5.7
Electromagnetic field
235
Notes
237
6
Effective action at finite temperature
238
6.1
Condensate contribution
238
6.2
Free homogeneous non-relativistic
Bose gas
241
6.3
Internal energy and specific heat
245
6.4
Bose
gas in a harmonic oscillator confining potential
247
6.5
Density of states method
258
6.6
Charged non-relativistic
Bose
gas in a constant
magnetic field
267
6.7
The interacting
Bose gas
278
6.8
The relativistic non-interacting charged scalar field
289
6.9
The interacting relativistic field
293
6.10
Fermi gases at finite temperature in a magnetic field
298
6.11
Trapped Fermi gases
309
Notes
322
7
Further applications of the
Schwinger
action principle
323
7.1
Integration of the action principle
323
7.2
Application of the action principle to the
free particle
325
Contents ix
7.3 Application
to the
simple
harmonic oscillator
329
7.4
Application to the forced harmonic oscillator
332
7.5
Propagators and energy levels
337
7.6
General variation of the Lagrangian
344
7.7
The vacuum-to-vacuum transition amplitude
348
7.8
More general systems
352
Notes
367
General definition of the effective action
368
8.1
Generating functionals for free field theory
368
8.2
Interacting fields and perturbation theory
374
8.3
Feynman diagrams
383
8.4
One-loop effective potential for a real scalar field
388
8.5
Dimensional regularization and the derivative expansion
394
8.6
Renormalization of
λφ4
theory
403
8.7
Finite temperature
415
8.8
Generalized CJT effective action
425
8.9
CJT approach to Bose-Einstein condensation
433
Notes
446
Appendix
1
Mathematical appendices
447
Appendix
2
Review of special relativity
462
Appendix
3
Interaction picture
469
Bibliography
479
Index
486
THE SCHWINGER
ACTION PRINCIPLE
AND EFFECTIVE ACTION
This book is an introduction to the
Schwinger
action principle in quan¬
tum mechanics and quantum field theory, with applications to a variety of
different models, not only those of interest to particle physics. The book
begins with a brief review of the action principle in classical mechan¬
ics and classical field theory. It then moves on to quantum field theory,
focusing on the effective action method. This is introduced as simply as
possible by using the zero-point energy of the simple harmonic oscilla¬
tor as the starting point. This allows the utility of the method, and the
process of regularization and renormalization of quantum field theory,
to be demonstrated with a minimum of formal development. The book
concludes with a more complete definition of the effective action, and
demonstrates how the provisional definition used earlier is the first term
in the systematic loop expansion.
Several applications of the
Schwinger
action principle are given,
including Bose-Einstein condensation, the
Casimir
effect, and trapped
Fermi gases. The renormalization of interacting scalar field theory is
presented to two-loop order. This book will interest graduate students
and researchers in theoretical physics who are familiar with quantum
mechanics.
David Toms is Reader in Mathematical Physics in the School of Math¬
ematics and Statistics at Newcastle University. Prior to joining New¬
castle University, Dr. Toms was a NATO Science Fellow at Imperial
College London, and a postdoctoral Fellow at the University of Wisconsin-
Milwaukee. His research interests include the formalism of quantum field
theory and its applications, and his most recent interests are centred
around Kaluza-Klein theory, based on the idea that there are extra spatial
dimensions beyond the three obvious ones.
|
| adam_txt |
Contents
Preface
page
χ
1
Action principle in classical mechanics
1
1.1
Euler-Lagrange equations
1
1.2
Hamilton's principle
5
1.3
Hamilton's equations
8
1.4
Canonical transformations
12
1.5
Conservation laws and symmetries
22
Notes
38
2
Action principle in classical field theory
40
2.1
Continuous systems
40
2.2
Lagrangian and Hamiltonian formulation for
continuous systems
43
2.3
Some examples
48
2.4
Functional differentiation and
Poisson
brackets for
field theory
54
2.5
Noether's theorem
60
2.6
The stress-energy-momentum tensor
66
2.7
Gauge
invariance
75
2.8
Fields of general spin
83
2.9
The Dirac equation
88
Notes
99
3
Action principle in quantum theory
100
3.1
States and
observables
100
3.2 Schwinger
action principle 111
3.3
Equations of motion and canonical commutation relations
113
3.4
Position and momentum eigenstates
120
3.5
Simple harmonic oscillator
124
3.6
Real scalar field
132
VII
viii Contents
3.7
Complex scalar
field
140
3.8 Schrödinger
field
144
3.9
Dirac field
151
3.10
Electromagnetic field
157
Notes
168
4
The effective action
169
4.1
Introduction
169
4.2
Free scalar field in Minkowski spacetime
174
4.3 Casimir
effect
178
4.4
Constant gauge field background
181
4.5
Constant magnetic field
186
4.6
Self-interacting scalar field
196
4.7
Local
Casimir
effect
203
Notes
207
5
Quantum statistical mechanics
208
5.1
Introduction
208
5.2
Simple harmonic oscillator
213
5.3
Real scalar field
217
5.4
Charged scalar field
221
5.5
Non-relativistic field
228
5.6
Dirac field
234
5.7
Electromagnetic field
235
Notes
237
6
Effective action at finite temperature
238
6.1
Condensate contribution
238
6.2
Free homogeneous non-relativistic
Bose gas
241
6.3
Internal energy and specific heat
245
6.4
Bose
gas in a harmonic oscillator confining potential
247
6.5
Density of states method
258
6.6
Charged non-relativistic
Bose
gas in a constant
magnetic field
267
6.7
The interacting
Bose gas
278
6.8
The relativistic non-interacting charged scalar field
289
6.9
The interacting relativistic field
293
6.10
Fermi gases at finite temperature in a magnetic field
298
6.11
Trapped Fermi gases
309
Notes
322
7
Further applications of the
Schwinger
action principle
323
7.1
Integration of the action principle
323
7.2
Application of the action principle to the
free particle
325
Contents ix
7.3 Application
to the
simple
harmonic oscillator
329
7.4
Application to the forced harmonic oscillator
332
7.5
Propagators and energy levels
337
7.6
General variation of the Lagrangian
344
7.7
The vacuum-to-vacuum transition amplitude
348
7.8
More general systems
352
Notes
367
General definition of the effective action
368
8.1
Generating functionals for free field theory
368
8.2
Interacting fields and perturbation theory
374
8.3
Feynman diagrams
383
8.4
One-loop effective potential for a real scalar field
388
8.5
Dimensional regularization and the derivative expansion
394
8.6
Renormalization of
λφ4
theory
403
8.7
Finite temperature
415
8.8
Generalized CJT effective action
425
8.9
CJT approach to Bose-Einstein condensation
433
Notes
446
Appendix
1
Mathematical appendices
447
Appendix
2
Review of special relativity
462
Appendix
3
Interaction picture
469
Bibliography
479
Index
486
THE SCHWINGER
ACTION PRINCIPLE
AND EFFECTIVE ACTION
This book is an introduction to the
Schwinger
action principle in quan¬
tum mechanics and quantum field theory, with applications to a variety of
different models, not only those of interest to particle physics. The book
begins with a brief review of the action principle in classical mechan¬
ics and classical field theory. It then moves on to quantum field theory,
focusing on the effective action method. This is introduced as simply as
possible by using the zero-point energy of the simple harmonic oscilla¬
tor as the starting point. This allows the utility of the method, and the
process of regularization and renormalization of quantum field theory,
to be demonstrated with a minimum of formal development. The book
concludes with a more complete definition of the effective action, and
demonstrates how the provisional definition used earlier is the first term
in the systematic loop expansion.
Several applications of the
Schwinger
action principle are given,
including Bose-Einstein condensation, the
Casimir
effect, and trapped
Fermi gases. The renormalization of interacting scalar field theory is
presented to two-loop order. This book will interest graduate students
and researchers in theoretical physics who are familiar with quantum
mechanics.
David Toms is Reader in Mathematical Physics in the School of Math¬
ematics and Statistics at Newcastle University. Prior to joining New¬
castle University, Dr. Toms was a NATO Science Fellow at Imperial
College London, and a postdoctoral Fellow at the University of Wisconsin-
Milwaukee. His research interests include the formalism of quantum field
theory and its applications, and his most recent interests are centred
around Kaluza-Klein theory, based on the idea that there are extra spatial
dimensions beyond the three obvious ones. |
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| id | DE-604.BV022969737 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:08:03Z |
| indexdate | 2024-07-09T21:08:50Z |
| institution | BVB |
| isbn | 9780521876766 |
| language | English |
| lccn | 2007013097 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016174002 |
| oclc_num | 122338040 |
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| owner_facet | DE-703 DE-91G DE-BY-TUM DE-11 DE-19 DE-BY-UBM |
| physical | XI, 495 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | Cambridge monographs on mathematical physics |
| spelling | Toms, David J. 1953- Verfasser (DE-588)139157107 aut The Schwinger action principle and effective action David J. Toms 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 XI, 495 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge monographs on mathematical physics Includes bibliographical references and index Mathematische Physik Quantentheorie Schwinger action principle Quantum theory Mathematical physics Schwinger-Modell (DE-588)4272231-7 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Schwinger-Modell (DE-588)4272231-7 s Quantenfeldtheorie (DE-588)4047984-5 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016174002&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016174002&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Toms, David J. 1953- The Schwinger action principle and effective action Mathematische Physik Quantentheorie Schwinger action principle Quantum theory Mathematical physics Schwinger-Modell (DE-588)4272231-7 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4272231-7 (DE-588)4047984-5 |
| title | The Schwinger action principle and effective action |
| title_auth | The Schwinger action principle and effective action |
| title_exact_search | The Schwinger action principle and effective action |
| title_exact_search_txtP | The Schwinger action principle and effective action |
| title_full | The Schwinger action principle and effective action David J. Toms |
| title_fullStr | The Schwinger action principle and effective action David J. Toms |
| title_full_unstemmed | The Schwinger action principle and effective action David J. Toms |
| title_short | The Schwinger action principle and effective action |
| title_sort | the schwinger action principle and effective action |
| topic | Mathematische Physik Quantentheorie Schwinger action principle Quantum theory Mathematical physics Schwinger-Modell (DE-588)4272231-7 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Mathematische Physik Quantentheorie Schwinger action principle Quantum theory Mathematical physics Schwinger-Modell Quantenfeldtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016174002&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016174002&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT tomsdavidj theschwingeractionprincipleandeffectiveaction |