Quantum field theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
De Gruyter
2013
|
| Series: | De Gruyter studies in mathematical physics
17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Revised Engl. translation of the 2003 Russian ed. of "Lectures on Quantum field theory" |
| Physical Description: | X, 409 S. graph. Darst. |
| ISBN: | 9783110270297 |
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MARC
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Record in the Search Index
| _version_ | 1804150192267591680 |
|---|---|
| adam_text | Contents
Preface
v
1 Basics
of elementary particles
1
1.1
Fundamental particles
..................................... 1
1.1.1
Fermions
........................................ 2
1.1.2
Vector bosons
..................................... 3
1.2
Fundamental interactions
.................................. 4
1.3
The Standard Model and perspectives
........................ 5
2 Lagrange
formalism. Symmetries and gauge fields
9
2.1 Lagrange
mechanics of a particle
............................ 9
2.2
Real scalar field.
Lagrange
equations
......................... 11
2.3
The Noether theorem
..................................... 15
2.4
Complex scalar and electromagnetic fields
.................... 18
2.5
Yang-Mills fields
........................................ 24
2.6
The geometry of gauge fields
............................... 30
2.7
A realistic example
-
chromodynamics
....................... 38
3
Canonical quantization, symmetries in quantum field theory
40
3.1
Photons
................................................ 40
3.1.1
Quantization of the electromagnetic field
............... 40
3.1.2
Remarks on gauge
invariance
and
Bose
statistics
......... 45
3.1.3
Vacuum fluctuations and
Casimir
effect
................ 48
3.2
Bosons
................................................ 50
3.2.1
Scalar particles
.................................... 50
3.2.2
Truly neutral particles
.............................. 54
3.2.3
C/T-transformations
.............................. 57
3.2.4
Vector bosons
..................................... 61
3.3
Fermions
............................................... 63
3.3.1
Three-dimensional spinors
........................... 63
3.3.2
Spinors of the
Lorentz
group
......................... 67
3.3.3
The Dirac equation
................................. 74
3.3.4
The algebra of Dirac s matrices
....................... 79
3.3.5
Plane waves
...................................... 81
Contents
3.3.6
Spin and statistics
.................................. 83
3.3.7
C, P, T
transformations for
fermions
.................. 85
3.3.8
Bilinear forms
.................................... 86
3.3.9
The neutrino
...................................... 87
The Feynman theory of positron and elementary quantum
electrodynamics
93
4.1
Nonrelativistic theory. Green s functions
...................... 93
4.2
Relativistic theory
........................................ 96
4.3
Momentum representation
................................. 100
4.4
The electron in an external electromagnetic field
................ 103
4.5
The two-particle problem
.................................. 110
Scattering matrix
115
5.1
Scattering amplitude
...................................... 115
5.2
Kinematic invariants
...................................... 118
5.3
Unitarity
............................................... 121
Invariant perturbation theory
124
6.1
Schroedinger and
Heisenberg
representations
..................124
6.2
Interaction representation
..................................125
6.3
S-matrix expansion
......................................128
6.4
Feynman diagrams for electron scattering in quantum
electrodynamics
.........................................135
6.5
Feynman diagrams for photon scattering
......................140
6.6
Electron propagator
......................................142
6.7
The photon propagator
....................................146
6.8
The Wick theorem and general diagram rules
..................149
Exact propagators and vertices
156
7.1
Field operators in the
Heisenberg
representation and interaction
representation
...........................................156
7.2
The exact propagator of photons
............................ 158
7.3
The exact propagator of electrons
........................... 164
7.4
Vertex parts
............................................ 168
7.5
Dyson equations
......................................... 172
7.6
Ward identity
........................................... 173
Contents ix
8
Some applications of quantum electrodynamics
175
8.1
Electron scattering by static charge: higher order corrections
......175
8.2
The Lamb shift and the anomalous magnetic moment
............180
8.3
Renormalization
-
how it works
.............................185
8.4
Running the coupling constant
............................189
8.5
Annihilation of e+e~ into hadrons. Proof of the existence of quarks
191
8.6
The physical conditions for renormalization
...................192
8.7
The classification and elimination of divergences
...............196
8.8
The asymptotic behavior of a photon propagator at large momenta
. 200
8.9
Relation between the bare and true charges
................203
8.10
The renormalization group in QED
..........................207
8.11
The asymptotic nature of a perturbation series
..................209
9
Path integrals and quantum mechanics
211
9.1
Quantum mechanics and path integrals
.......................211
9.2
Perturbation theory
.......................................219
9.3
Functional derivatives
....................................225
9.4
Some properties of functional integrals
.......................226
10
Functional integrals: scalars and spinors
232
10.1
Generating the functional for scalar fields
.....................232
10.2
Functional integration
.....................................237
10.3
Free particle Green s functions
.............................240
10.4
Generating the functional for interacting fields
.................247
10.5
φ4
theory
...............................................250
10.6
The generating functional for connected diagrams
..............257
10.7
Self-energy and vertex functions
............................260
10.8
The theory of critical phenomena
............................264
10.9
Functional methods for
fermions
............................277
10.10
Propagators and gauge conditions in QED
.....................285
11
Functional integrals: gauge fields
287
11.1
Non-Abelian gauge fields and Faddeev-Popov quantization
.......287
11.2
Feynman diagrams for non-Abelian theory
....................293
χ
Contents
12 The Weinberg-Salam
model
302
12.1
Spontaneous symmetry-breaking and the
Goldstone
theorem
......302
12.2
Gauge fields and the Higgs phenomenon
......................308
12.3
Yang-Mills fields and spontaneous symmetry-breaking
..........311
12.4
The Weinberg-Salam model
...............................317
13
Renormalization
326
13.1
Divergences in
ψ4
........................................326
13.2
Dimensional regularization of ^-theory
......................330
13.3
Renormalization of ^>4-theory
..............................335
13.4
The renormalization group
.................................342
13.5
Asymptotic freedom of the Yang-Mills theory
.................348
13.6
Running coupling constants and the grand unification
........355
14
Nonperturbative approaches
361
14.1
The lattice field theory
....................................361
14.2
Effective potential and loop expansion
.......................373
14.3 Instantons in
quantum mechanics
............................378
14.4
Instantons
and the unstable vacuum in field theory
..............389
14.5
The Lipatov asymptotics of a perturbation series
................395
14.6
The end of the zero-charge story?
..........................397
Bibliography
402
Index
406
This book discusses the main concepts of the Standard Model of elementary particles in
a compact and straightforward way. The work illustrates the unity of modern theoretical
physics by combining approaches and concepts of the quantum field theory and modem
condensed matter theory. The inductive approach allows a deep understanding of ideas
and methods used for solving problems in this field.
The series is devoted to the publication of monographs and high-level texts in mathe¬
matical physics. They cover topics and methods in fields of current interest, with
an emphasis on didactical presentation. The series will enable readers to understand,
apply, and develop further, with sufficient rigor, mathematical methods to given
problems in physics. For this reason, works with a few authors are preferred over
edited volumes. The works in this series are aimed at advanced students and
researchers in mathematical and theoretical physics. They can also serve as secondary
reading for lectures and seminars at advanced levels.
/w.degruyter.com
ISBN
978-3-11-027029-7
|
| any_adam_object | 1 |
| author | Sadovskii, Michail V. 1948- |
| author_GND | (DE-588)1027151760 |
| author_facet | Sadovskii, Michail V. 1948- |
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| author_sort | Sadovskii, Michail V. 1948- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.143 |
| dewey-search | 530.143 |
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| dewey-tens | 530 - Physics |
| discipline | Physik |
| era | Geschichte 1959-1975 gnd |
| era_facet | Geschichte 1959-1975 |
| format | Book |
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| spelling | Sadovskii, Michail V. 1948- Verfasser (DE-588)1027151760 aut Quantum field theory Michael V. Sadovskii Berlin [u.a.] De Gruyter 2013 X, 409 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematical physics 17 Revised Engl. translation of the 2003 Russian ed. of "Lectures on Quantum field theory" Geschichte 1959-1975 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1998 Ringberg Tegernsee gnd-content (DE-588)4135952-5 Quelle gnd-content Quantenfeldtheorie (DE-588)4047984-5 s DE-604 Geschichte 1959-1975 z Erscheint auch als Online-Ausgabe 978-3-11-027035-8 De Gruyter studies in mathematical physics 17 (DE-604)BV040141722 17 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025886960&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=025886960&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Sadovskii, Michail V. 1948- Quantum field theory De Gruyter studies in mathematical physics Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)1071861417 (DE-588)4135952-5 |
| title | Quantum field theory |
| title_auth | Quantum field theory |
| title_exact_search | Quantum field theory |
| title_full | Quantum field theory Michael V. Sadovskii |
| title_fullStr | Quantum field theory Michael V. Sadovskii |
| title_full_unstemmed | Quantum field theory Michael V. Sadovskii |
| title_short | Quantum field theory |
| title_sort | quantum field theory |
| topic | Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Quantenfeldtheorie Konferenzschrift 1998 Ringberg Tegernsee Quelle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025886960&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=025886960&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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