Lectures on quantum field theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey u. a.
World Scientific
2008
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 775 S. graph. Darst. |
| ISBN: | 9812832858 9789812832856 9812832866 9789812832863 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
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| 008 | 081201s2008 d||| |||| 00||| eng d | ||
| 020 | |a 9812832858 |c hbd. |9 981-283285-8 | ||
| 020 | |a 9789812832856 |c hbd. |9 978-981-283285-6 | ||
| 020 | |a 9812832866 |c pbk. |9 981-283286-6 | ||
| 020 | |a 9789812832863 |c pbk. |9 978-981-283286-3 | ||
| 035 | |a (OCoLC)609849235 | ||
| 035 | |a (DE-599)GBV578850575 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-384 |a DE-355 |a DE-20 |a DE-29T |a DE-11 |a DE-19 | ||
| 082 | 0 | |a 530.143 | |
| 084 | |a UO 4000 |0 (DE-625)146237: |2 rvk | ||
| 084 | |a PHY 023f |2 stub | ||
| 100 | 1 | |a Das, Ashok |d 1953- |e Verfasser |0 (DE-588)13395157X |4 aut | |
| 245 | 1 | 0 | |a Lectures on quantum field theory |c Ashok Das |
| 246 | 1 | 3 | |a Quantum field theory |
| 264 | 1 | |a New Jersey u. a. |b World Scientific |c 2008 | |
| 300 | |a XIII, 775 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Quantenfeldtheorie |0 (DE-588)4047984-5 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Quantenfeldtheorie |0 (DE-588)4047984-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016995980&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016995980 | ||
Datensatz im Suchindex
| _version_ | 1804138366810193920 |
|---|---|
| adam_text | Contents
Preface
................................
vii
1
Relativistic
equations
..................... 1
1.1
Introduction
....................... 1
1.2
Notations
......................... 2
1.3
Klein-Gordon equation
................. 10
1.3.1
Klein paradox
................... 14
1.4
Dirac equation
...................... 19
1.5
References
........................ 26
2
Solutions of the Dirac equation
................ 27
2.1
Plane wave solutions
.................. 27
2.2
Normalization of the wave function
.......... 34
2.3
Spin of the Dirac particle
................ 40
2.4
Continuity equation
................... 44
2.5
Dirac s hole theory
................... 47
2.6
Properties of the Dirac matrices
............ 49
2.6.1
Fierz rearrangement
............... 58
2.7
References
........................ 62
3
Properties of the Dirac equation
............... 65
3.1
Lorentz
transformations
................ 65
3.2
Covariance of the Dirac equation
........... 72
3.3
Transformation of bilinears
............... 82
3.4
Projection operators, completeness relation
..... 84
3.5
Helicity
.......................... 92
3.6
Massless Dirac particle
................. 94
3.7
Chirality
......................... 99
3.8
Non-relativistic limit of the Dirac equation
...... 105
3.9
Electron in an external magnetic field
........ 107
3.10
Foldy-Wouthuysen transformation
...........
Ill
ix
x
Contents
3.11 Zitterbewegung.....................117
3.12
References
........................122
4
Representations of
Lorentz
and
Poincaré
groups
......125
4.1
Symmetry algebras
...................125
4.1.1
Rotation
...................... 125
4.1.2
Translation
.................... 129
4.1.3
Lorentz
transformation
............. 130
4.1.4
Poincaré
transformation
............. 133
4.2
Representations of the
Lorentz
group
......... 135
4.2.1
Similarity transformations and representations
140
4.3
Unitary representations of the
Poincaré
group
.... 147
4.3.1
Massive representation
..............151
4.3.2
Massless representation
.............155
4.4
References
........................160
5
Free Klein-Gordon field theory
................161
5.1
Introduction
....................... 161
5.2
Lagrangian density
................... 163
5.3
Quantization
....................... 167
5.4
Field decomposition
................... 171
5.5
Creation and annihilation operators
.......... 175
5.6
Energy eigenstates
................... 186
5.7
Physical meaning of energy eigenstates
........ 190
5.8
Green s functions
.................... 194
5.9
Covariant commutation relations
........... 205
5.10
References
........................ 209
6
Self-interacting scalar field theory
..............211
6.1 Nöther s
theorem
.................... 211
6.1.1
Space-time translation
.............. 215
6.2
Self-interacting
φΑ
theory
................ 219
6.3
Interaction picture and time evolution operator
. . . 223
6.4
S-matrix
......................... 229
6.5
Normal ordered product and Wick s theorem
.... 233
6.6
Time ordered products and Wick s theorem
..... 241
6.7
Spectral representation and dispersion relation
. . . 246
6.8
References
........................ 254
Contents
xi
7
Complex scalar field theory
..................257
7.1
Quantization
.......................257
7.2
Field decomposition
...................260
7.3
Charge operator
.....................263
7.4
Green s functions
....................268
7.5
Spontaneous symmetry breaking and the
Goldstone
theorem
.........................270
7.6
Electromagnetic coupling
................281
7.7
References
........................283
8
Dirac field theory
........................285
8.1 Pauli
exclusion principle
................285
8.2
Quantization of the Dirac field
.............286
8.3
Field decomposition
...................291
8.4
Charge operator
.....................297
8.5
Green s functions
....................300
8.6
Covariant anti-commutation relations
.........303
8.7
Normal ordered and time ordered products
.....305
8.8
Massless Dirac fields
..................308
8.9
Yukawa interaction
...................312
8.10
Feynman diagrams
...................318
8.11
References
........................325
9
Maxwell field theory
......................327
9.1
Maxwell s equations
...................327
9.2
Canonical quantization
.................330
9.3
Field decomposition
...................335
9.4
Photon propagator
...................342
9.5
Quantum electrodynamics
...............347
9.6
Physical processes
....................350
9.7
Ward-Takahashi identity in QED
...........355
9.8
Covariant quantization of the Maxwell theory
.... 360
9.9
References
........................376
10
Dirac method for constrained systems
............379
10.1
Constrained systems
..................379
10.2
Dirac method and Dirac bracket
............384
10.3
Particle moving on a sphere
..............390
10.4
Reiativistic particle
...................395
10.5
Dirac field theory
....................401
10.6
Maxwell field theory
..................407
xii
Contents
10.7
References
........................413
11
Discrete symmetries
......................415
11.1
Parity
...........................415
11.1.1
Parity in quantum mechanics
..........417
11.1.2
Spin zero field
..................424
11.1.3
Photon field
....................428
11.1.4
Dirac field
.....................429
11.2
Charge conjugation
...................436
11.2.1
Spin zero field
..................437
11.2.2
Dirac field
.....................441
11.2.3
Majorana
fermions................
449
11.2.4
Eigenstates of charge conjugation
........453
11.3
Time reversal
......................458
11.3.1
Spin zero field and Maxwell s theory
...... 464
11.3.2
Dirac fields
.................... 467
11.3.3
Consequences of
T
invariance..........
473
11.3.4
Electric
dipole
moment of neutron
....... 477
11.4
CVT theorem
...................... 479
11.4.1
Equality of mass for particles and antiparticles
479
11.4.2
Electric charge for particles and antiparticles
. 480
11.4.3
Equality of lifetimes for particles and antipar¬
ticles
........................480
11.5
References
........................482
12
Yang-Mills theory
.......................485
12.1
Non-Abelian gauge theories
.............. 485
12.2
Canonical quantization of Yang-Mills theory
..... 502
12.3
Path integral quantization of gauge theories
..... 512
12.4
Path integral quantization of tensor fields
...... 530
12.5
References
........................ 542
13
BRST
invariance
and its consequences
............545
13.1
BRST
symmetry
.................... 545
13.2
Covariant quantization of Yang-Mills theory
..... 550
13.3
Unitarity
......................... 561
13.4
Slavnov-Taylor identity
................. 565
13.5
Feynman rules
...................... 571
13.6
Ghost free gauges
.................... 578
13.7
References
........................ 581
Contents
xiii
14
Higgs phenomenon and the standard model
.........583
14.1 Stückelberg
formalism
.................583
14.2
Higgs phenomenon
...................589
14.3
The standard model
...................596
14.3.1
Field content
................... 599
14.3.2
Lagrangian density
................ 601
14.3.3
Spontaneous symmetry breaking
........ 605
14.4
References
........................ 616
15
Regularization of Feynman diagrams
.............619
15.1
Introduction
.......................619
15.2
Loop expansion
.....................621
15.3
Cut-off regularization
..................623
15.3.1
Calculation in the Yukawa theory
........631
15.4 Pauli-Villars
regularization
...............638
15.5
Dimensional regularization
...............647
15.5.1
Calculations in QED
...............656
15.6
References
........................666
16
Renormalization theory
....................669
16.1
Superficial degree of divergence
............ 669
16.2
A brief history of renormalization
........... 679
16.3
Schwinger-Dyson equation
............... 690
16.4
BPHZ renormalization
................. 692
16.5
Renormalization of gauge theories
........... 721
16.6
Anomalous Ward identity
............... 724
16.7
References
........................ 732
17
Renormalization group and equation
.............733
17.1
Gell-Mann-Low equation
................ 733
17.2
Renormalization group
................. 739
17.3
Renormalization group equation
............ 744
17.4
Solving the renormalization group equation
..... 748
17.5
Callan-Symanzik equation
............... 759
17.6
References
........................ 766
Index
................................. 769
|
| adam_txt |
Contents
Preface
.
vii
1
Relativistic
equations
. 1
1.1
Introduction
. 1
1.2
Notations
. 2
1.3
Klein-Gordon equation
. 10
1.3.1
Klein paradox
. 14
1.4
Dirac equation
. 19
1.5
References
. 26
2
Solutions of the Dirac equation
. 27
2.1
Plane wave solutions
. 27
2.2
Normalization of the wave function
. 34
2.3
Spin of the Dirac particle
. 40
2.4
Continuity equation
. 44
2.5
Dirac's hole theory
. 47
2.6
Properties of the Dirac matrices
. 49
2.6.1
Fierz rearrangement
. 58
2.7
References
. 62
3
Properties of the Dirac equation
. 65
3.1
Lorentz
transformations
. 65
3.2
Covariance of the Dirac equation
. 72
3.3
Transformation of bilinears
. 82
3.4
Projection operators, completeness relation
. 84
3.5
Helicity
. 92
3.6
Massless Dirac particle
. 94
3.7
Chirality
. 99
3.8
Non-relativistic limit of the Dirac equation
. 105
3.9
Electron in an external magnetic field
. 107
3.10
Foldy-Wouthuysen transformation
.
Ill
ix
x
Contents
3.11 Zitterbewegung.117
3.12
References
.122
4
Representations of
Lorentz
and
Poincaré
groups
.125
4.1
Symmetry algebras
.125
4.1.1
Rotation
. 125
4.1.2
Translation
. 129
4.1.3
Lorentz
transformation
. 130
4.1.4
Poincaré
transformation
. 133
4.2
Representations of the
Lorentz
group
. 135
4.2.1
Similarity transformations and representations
140
4.3
Unitary representations of the
Poincaré
group
. 147
4.3.1
Massive representation
.151
4.3.2
Massless representation
.155
4.4
References
.160
5
Free Klein-Gordon field theory
.161
5.1
Introduction
. 161
5.2
Lagrangian density
. 163
5.3
Quantization
. 167
5.4
Field decomposition
. 171
5.5
Creation and annihilation operators
. 175
5.6
Energy eigenstates
. 186
5.7
Physical meaning of energy eigenstates
. 190
5.8
Green's functions
. 194
5.9
Covariant commutation relations
. 205
5.10
References
. 209
6
Self-interacting scalar field theory
.211
6.1 Nöther's
theorem
. 211
6.1.1
Space-time translation
. 215
6.2
Self-interacting
φΑ
theory
. 219
6.3
Interaction picture and time evolution operator
. . . 223
6.4
S-matrix
. 229
6.5
Normal ordered product and Wick's theorem
. 233
6.6
Time ordered products and Wick's theorem
. 241
6.7
Spectral representation and dispersion relation
. . . 246
6.8
References
. 254
Contents
xi
7
Complex scalar field theory
.257
7.1
Quantization
.257
7.2
Field decomposition
.260
7.3
Charge operator
.263
7.4
Green's functions
.268
7.5
Spontaneous symmetry breaking and the
Goldstone
theorem
.270
7.6
Electromagnetic coupling
.281
7.7
References
.283
8
Dirac field theory
.285
8.1 Pauli
exclusion principle
.285
8.2
Quantization of the Dirac field
.286
8.3
Field decomposition
.291
8.4
Charge operator
.297
8.5
Green's functions
.300
8.6
Covariant anti-commutation relations
.303
8.7
Normal ordered and time ordered products
.305
8.8
Massless Dirac fields
.308
8.9
Yukawa interaction
.312
8.10
Feynman diagrams
.318
8.11
References
.325
9
Maxwell field theory
.327
9.1
Maxwell's equations
.327
9.2
Canonical quantization
.330
9.3
Field decomposition
.335
9.4
Photon propagator
.342
9.5
Quantum electrodynamics
.347
9.6
Physical processes
.350
9.7
Ward-Takahashi identity in QED
.355
9.8
Covariant quantization of the Maxwell theory
. 360
9.9
References
.376
10
Dirac method for constrained systems
.379
10.1
Constrained systems
.379
10.2
Dirac method and Dirac bracket
.384
10.3
Particle moving on a sphere
.390
10.4
Reiativistic particle
.395
10.5
Dirac field theory
.401
10.6
Maxwell field theory
.407
xii
Contents
10.7
References
.413
11
Discrete symmetries
.415
11.1
Parity
.415
11.1.1
Parity in quantum mechanics
.417
11.1.2
Spin zero field
.424
11.1.3
Photon field
.428
11.1.4
Dirac field
.429
11.2
Charge conjugation
.436
11.2.1
Spin zero field
.437
11.2.2
Dirac field
.441
11.2.3
Majorana
fermions.
449
11.2.4
Eigenstates of charge conjugation
.453
11.3
Time reversal
.458
11.3.1
Spin zero field and Maxwell's theory
. 464
11.3.2
Dirac fields
. 467
11.3.3
Consequences of
T
invariance.
473
11.3.4
Electric
dipole
moment of neutron
. 477
11.4
CVT theorem
. 479
11.4.1
Equality of mass for particles and antiparticles
479
11.4.2
Electric charge for particles and antiparticles
. 480
11.4.3
Equality of lifetimes for particles and antipar¬
ticles
.480
11.5
References
.482
12
Yang-Mills theory
.485
12.1
Non-Abelian gauge theories
. 485
12.2
Canonical quantization of Yang-Mills theory
. 502
12.3
Path integral quantization of gauge theories
. 512
12.4
Path integral quantization of tensor fields
. 530
12.5
References
. 542
13
BRST
invariance
and its consequences
.545
13.1
BRST
symmetry
. 545
13.2
Covariant quantization of Yang-Mills theory
. 550
13.3
Unitarity
. 561
13.4
Slavnov-Taylor identity
. 565
13.5
Feynman rules
. 571
13.6
Ghost free gauges
. 578
13.7
References
. 581
Contents
xiii
14
Higgs phenomenon and the standard model
.583
14.1 Stückelberg
formalism
.583
14.2
Higgs phenomenon
.589
14.3
The standard model
.596
14.3.1
Field content
. 599
14.3.2
Lagrangian density
. 601
14.3.3
Spontaneous symmetry breaking
. 605
14.4
References
. 616
15
Regularization of Feynman diagrams
.619
15.1
Introduction
.619
15.2
Loop expansion
.621
15.3
Cut-off regularization
.623
15.3.1
Calculation in the Yukawa theory
.631
15.4 Pauli-Villars
regularization
.638
15.5
Dimensional regularization
.647
15.5.1
Calculations in QED
.656
15.6
References
.666
16
Renormalization theory
.669
16.1
Superficial degree of divergence
. 669
16.2
A brief history of renormalization
. 679
16.3
Schwinger-Dyson equation
. 690
16.4
BPHZ renormalization
. 692
16.5
Renormalization of gauge theories
. 721
16.6
Anomalous Ward identity
. 724
16.7
References
. 732
17
Renormalization group and equation
.733
17.1
Gell-Mann-Low equation
. 733
17.2
Renormalization group
. 739
17.3
Renormalization group equation
. 744
17.4
Solving the renormalization group equation
. 748
17.5
Callan-Symanzik equation
. 759
17.6
References
. 766
Index
. 769 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Das, Ashok 1953- |
| author_GND | (DE-588)13395157X |
| author_facet | Das, Ashok 1953- |
| author_role | aut |
| author_sort | Das, Ashok 1953- |
| author_variant | a d ad |
| building | Verbundindex |
| bvnumber | BV035189340 |
| classification_rvk | UO 4000 |
| classification_tum | PHY 023f |
| ctrlnum | (OCoLC)609849235 (DE-599)GBV578850575 |
| dewey-full | 530.143 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.143 |
| dewey-search | 530.143 |
| dewey-sort | 3530.143 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV035189340 |
| illustrated | Illustrated |
| index_date | 2024-07-02T23:01:09Z |
| indexdate | 2024-07-09T21:27:03Z |
| institution | BVB |
| isbn | 9812832858 9789812832856 9812832866 9789812832863 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016995980 |
| oclc_num | 609849235 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-355 DE-BY-UBR DE-20 DE-29T DE-11 DE-19 DE-BY-UBM |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-355 DE-BY-UBR DE-20 DE-29T DE-11 DE-19 DE-BY-UBM |
| physical | XIII, 775 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Das, Ashok 1953- Verfasser (DE-588)13395157X aut Lectures on quantum field theory Ashok Das Quantum field theory New Jersey u. a. World Scientific 2008 XIII, 775 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Quantenfeldtheorie (DE-588)4047984-5 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016995980&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Das, Ashok 1953- Lectures on quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4123623-3 |
| title | Lectures on quantum field theory |
| title_alt | Quantum field theory |
| title_auth | Lectures on quantum field theory |
| title_exact_search | Lectures on quantum field theory |
| title_exact_search_txtP | Lectures on quantum field theory |
| title_full | Lectures on quantum field theory Ashok Das |
| title_fullStr | Lectures on quantum field theory Ashok Das |
| title_full_unstemmed | Lectures on quantum field theory Ashok Das |
| title_short | Lectures on quantum field theory |
| title_sort | lectures on quantum field theory |
| topic | Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Quantenfeldtheorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016995980&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT dasashok lecturesonquantumfieldtheory AT dasashok quantumfieldtheory |