A first book of quantum field theory
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford, U.K.
Alpha Science International
2007
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| Ausgabe: | 2. ed., 2. reprint |
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| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV035743273 | ||
| 003 | DE-604 | ||
| 005 | 20100210 | ||
| 007 | t | ||
| 008 | 090928s2007 d||| |||| 00||| eng d | ||
| 020 | |a 9781842652497 |9 978-1-84265-249-7 | ||
| 035 | |a (OCoLC)254581588 | ||
| 035 | |a (DE-599)HBZHT014997908 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-703 | ||
| 050 | 0 | |a QC174.45 | |
| 082 | 0 | |a 530.14/3 | |
| 084 | |a UO 4000 |0 (DE-625)146237: |2 rvk | ||
| 100 | 1 | |a Lahiri, Amitabha |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A first book of quantum field theory |c Amitabha Lahiri ; Palash B. Pal |
| 250 | |a 2. ed., 2. reprint | ||
| 264 | 1 | |a Oxford, U.K. |b Alpha Science International |c 2007 | |
| 300 | |a XVII, 380 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes index | ||
| 650 | 0 | 7 | |a Quantenfeldtheorie |0 (DE-588)4047984-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Quantenfeldtheorie |0 (DE-588)4047984-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Pal, Palash B. |d 1955- |e Verfasser |0 (DE-588)13127290X |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018603461&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018603461 | ||
Datensatz im Suchindex
| _version_ | 1804140656604479488 |
|---|---|
| adam_text | Contents
Preface
to the second edition
v
Preface to the first edition
vii
Notations
xi
1
Preliminaries
1
1.1
Why Quantum Field Theory
................. 1
1.2
Creation and annihilation operators
............. 3
1.3
Special relativity
........................ 5
1.4
Space and time in relativistic quantum theory
........ 8
1.5
Natural units
.......................... 9
2
Classical Field Theory
12
2.1
A quick review of particle mechanics
............. 12
2.1.1
Action principle and Euler-Lagrange equations
... 12
2.1.2
Hamiltonian formalism and
Poisson
brackets
.... 14
2.2
Euler-Lagrange equations in field theory
........... 15
2.2.1
Action functional and Lagrangian
.......... 15
2.2.2
Euler-Lagrange equations
............... 17
2.3
Hamiltonian formalism
..................... 19
2.4
Noether s theorem
....................... 21
S
Quantization of scalar fields
28
3.1
Equation of motion
....................... 28
3.2
The field and its canonical quantization
........... 29
3.3
Fourier decomposition of the field
............... 30
3.4
Ground state of the Hamiltonian and normal ordering
... 34
3.5
Fock space
............................ 36
3.6
Complex scalar field
....................... 37
3.6.1
Creation and annihilation operators
......... 37
3.6.2
Particles and antiparticles
............... 39
3.6.3
Ground state and Hamiltonian
............ 40
3.7
Propagator
........................... 41
ХШ
xiv Contents
4
Quantization of Dirac fields
47
4.1
Dirac Hamiltonian
....................... 47
4.2
Dirac equation
......................... 51
4.3
Plane wave solutions of Dirac equation
............ 54
4.3.1
Positive and negative energy spinors
......... 54
4.3.2
Explicit solutions in Dirac-Pauli representation
... 56
4.4
Projection operators
...................... 59
4.4.1
Projection operators for positive and negative energy
states
.......................... 59
4.4.2
Helicity
projection operators
............. 60
4.4.3
Chirality projection operators
............. 61
4.4.4
Spin projection operators
............... 62
4.5
Lagrangian for a Dirac field
.................. 63
4.6
Fourier decomposition of the field
............... 65
4.7
Propagator
........................... 69
5
The S-matrix expansion
72
5.1
Examples of interactions
.................... 73
5.2
Evolution operator
....................... 75
5.3
S-matrix
............................. 80
5.4
Wick s theorem
......................... 82
6
Prom Wick expansion to Feynman diagrams
87
6.1
Yukawa interaction
:
decay of a scalar
............ 87
6.2
Normalized states
..................... · . 94
6.3
Sample calculation of a matrix element
............ 97
6.4
Another example: fermion scattering
............. 101
6.5
Feynman amplitude
...................... 105
6.6
Feynman rules
......................... 106
6.7
Virtual particles
........................ 110
6.8
Amplitudes which are not S-matrix elements
........ 112
7
Cross sections and decay rates
115
7.1
Decay rate
............................ 115
7.2
Examples of decay rate calculation
.............. 117
7.2.1
Decay of a scalar into a fermion-antifermion pair
. . 117
7.2.2
Muon decay with 4-fermion interaction
........ 122
7.3
Scattering cross section
.................... 130
7.4
Generalities of
2-ÍO-2
scattering
................ 133
7.4.1
CM frame
........................ 135
7.4.2
Lab frame
........................ 137
7.5
Inelastic scattering with 4-fermion interaction
........ 140
7.5.1
Cross-section in CM frame
.............. 142
7.5.2
Cross-section in Lab frame
.............. 143
7.6
Mandelstam
variables
..................... 144
Contents xv
8
Quantization of the electromagnetic field
146
8.1
Classical theory of electromagnetic fields
........... 146
8.2
Problems with quantization
.................. 149
8.3
Modifying the classical Lagrangian
.............. 150
8.4
Propagator
........................... 153
8.5
Fourier decomposition of the field
............... 156
8.6
Physical states
......................... 158
8.7
Another look at the propagator
................ 162
8.8
Feynman rules for photons
................... 164
9
Quantum electrodynamics
166
9.1
Local gauge
invariance
..................... 166
9.2
Interaction Hamiltonian
.................... 170
9.3
Lowest order processes
..................... 172
9.4
Electron-electron scattering
.................. 174
9.5
Electron-positron scattering
.................. 180
9.6
e-e*
-»
μ~μ+
......................... 182
9.7
Consequence of gauge
invariance
............... 184
9.8
Compton scattering
...................... 185
9.9
Scattering by an external field
................. 194
9.10 Bremsstrahlung......................... 197
10
P, T, C
and their combinations
200
10.1
Motivations from classical physics
............... 200
10.2
Parity
.............................. 201
10.2.1
Free scalar fields
.................... 201
10.2.2
Free Dirac field
..................... 202
10.2.3
Free photon field
.................... 204
10.2.4
Interacting fields
.................... 205
10.3
Charge conjugation
....................... 207
10.3.1
Free fields
........................ 207
10.3.2
Interactions
....................... 211
10.4
Time reversal
.......................... 212
10.4.1
Antilinearity
...................... 212
10.4.2
Free fields
........................ 213
10.4.3
Interactions
....................... 216
10.5
CP
................................ 217
10.6
CPT
..........■..................... 218
11
Electromagnetic form factors
222
11.1
General electromagnetic vertex
................ 222
11.2
Physical interpretation of form factors
............ 224
11.2.1
Charge form factor
Fi
................. 224
11.2.2
Anomalous magnetic moment Fa
........... 228
11.2.3
Electric
dipole
moment F2
............... 228
xvi
Contents
11.2.4 Anapole
moment F3
.................. 229
11.3
Anomalous magnetic moment of the electron
........ 230
11.4
Charge form factor
....................... 239
11.5
Electron-proton scattering
................... 241
12
Renormalization
245
12.1
Degree of divergence of a diagram
.............. 245
12.1.1
Superficial degree of divergence
............ 245
12.1.2
Superficial vs. real degree of divergence
....... 248
12.2
Specific examples in QED
................... 250
12.3
Outline of the program
..................... 252
12.4
Ward-Takahashi identity
.................... 253
12.5
General forms for divergent amplitudes
............ 256
12.5.1
Fermion self-energy
................... 256
12.5.2
Vacuum polarization
.................. 257
12.5.3
Vertex function^
..................... 259
12.6
Regularization of self-energy diagrams
............ 260
12.6.1
Vacuum polarization diagram
............. 260
12.6.2
Fermion self-energy diagram
.............. 265
12.7
Counterterms
.......................... 267
12.7.1
Vacuum polarization diagram
............. 267
12.7.2
Fermion self-energy diagram
.............. 270
12.7.3
Vertex function
..................... 272
12.8
Full Lagrangian
......................... 273
12.9
Observable effects of renormalization
............. 275
12.9.1
Modification of Coulomb interaction
......... 275
12.9.2
Running coupling constant
.............. 276
12.9.3
Cancellation of infra-red divergences
......... 279
13
Symmetries and symmetry breaking
283
13.1
Classification of symmetries
.................. 283
13.2
Groups and symmetries
.................... 284
13.2.1
Symmetry group
.................... 284
13.2.2
Examples of continuous symmetry groups
...... 286
13.2.3
Generators of continuous groups
........... 289
13.2.4
Representations
..................... 292
13.3
Approximate symmetries
.................... 293
13.4
Spontaneous breaking of symmetries
............. 294
13.4.1
Discrete symmetry
................... 295
13.4.2
U(l) symmetry
. .................... 299
13.4.3
Non-Abelian symmetry
...... . . ........ 300
13.5
Goldstone s theorem
...................... 301
13.5.1
Appearance of masskss states
. . . .......... 301
13.5.2
Examples of Nambu-Goldstone bosons
. ....... 303
Contents xvii
13.5.3
Interaction
of
Goldstone
bosons
............ 305
13.6
Higgs mechanism
........................ 308
1Ą
Yang-Mills theory of non-Abelian gauge fields
312
14.1
Gauge fields of non-Abelian symmetry
............ 312
14.2
Pure gauge Lagrangian
...................... 315
14.3
Interactions of non-Abelian gauge fields
........... 318
14.3.1
Gauge interactions of other particles
......... 318
14.3.2
Self-interactions of gauge bosons
........... 319
14.4
Equations of motion and conserved currents
......... 321
14.5
Quantization of non-Abelian gauge fields
........... 322
14.6
Quantum Chromodynamics
.................. 323
15
Standard electroweak theory
326
15.1
Gauge group
.......................... 326
15.1.1
Choice of gauge group
................. 326
15.1.2
Pure gauge Lagrangian
................ 328
15.2
Spontaneous symmetry breaking
............... 330
15.2.1
Introducing the Higgs boson
multiplet
.....: . . 330
15.2.2
Gauge boson masses
.................. 332
15.2.3
Scalar modes
...................... 333
15.3
Fermions
in the theory
..................... 335
15.3.1
Gauge interactions
................... 335
15.3.2
Electron mass
...................... 338
15.3.3
Yukawa couplings
.................... 339
15.3.4
Other
fermions
in the model
............. 340
15.4
Gauge boson decay
....................... 342
15.5
Scattering processes
...................... 346
15.5.1
Forward-backward asymmetry
............ 346
15.5.2
Low energy weak interactions
............. 349
15.5.3
High energy scattering
................. 351
15.6
Propagator for unstable particles
............... 355
15.7
Global symmetries of the model
................ 356
A Useful formulas
358
A.1 Representation of 7-matrices
................. 358
A.2 Traces of 7-matrices
...................... 360
A.3 The antisymmetric tensor
................... 363
A.4 Useful integration formulas
.................. 364
A.4.1 Angular integrations in iV-dimensional space
.... 364
A.4.2 Momentum integration in loops
............ 366
В
Answers to selected exercises
368
Index
371
|
| any_adam_object | 1 |
| author | Lahiri, Amitabha Pal, Palash B. 1955- |
| author_GND | (DE-588)13127290X |
| author_facet | Lahiri, Amitabha Pal, Palash B. 1955- |
| author_role | aut aut |
| author_sort | Lahiri, Amitabha |
| author_variant | a l al p b p pb pbp |
| building | Verbundindex |
| bvnumber | BV035743273 |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.45 |
| callnumber-search | QC174.45 |
| callnumber-sort | QC 3174.45 |
| callnumber-subject | QC - Physics |
| classification_rvk | UO 4000 |
| ctrlnum | (OCoLC)254581588 (DE-599)HBZHT014997908 |
| dewey-full | 530.14/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.14/3 |
| dewey-search | 530.14/3 |
| dewey-sort | 3530.14 13 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 2. ed., 2. reprint |
| format | Book |
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| id | DE-604.BV035743273 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:03:27Z |
| institution | BVB |
| isbn | 9781842652497 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018603461 |
| oclc_num | 254581588 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XVII, 380 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Alpha Science International |
| record_format | marc |
| spelling | Lahiri, Amitabha Verfasser aut A first book of quantum field theory Amitabha Lahiri ; Palash B. Pal 2. ed., 2. reprint Oxford, U.K. Alpha Science International 2007 XVII, 380 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes index Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 s DE-604 Pal, Palash B. 1955- Verfasser (DE-588)13127290X aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018603461&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lahiri, Amitabha Pal, Palash B. 1955- A first book of quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4047984-5 |
| title | A first book of quantum field theory |
| title_auth | A first book of quantum field theory |
| title_exact_search | A first book of quantum field theory |
| title_full | A first book of quantum field theory Amitabha Lahiri ; Palash B. Pal |
| title_fullStr | A first book of quantum field theory Amitabha Lahiri ; Palash B. Pal |
| title_full_unstemmed | A first book of quantum field theory Amitabha Lahiri ; Palash B. Pal |
| title_short | A first book of quantum field theory |
| title_sort | a first book of quantum field theory |
| topic | Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Quantenfeldtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018603461&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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