Quantum field theory for the gifted amateur:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2014
|
| Ausgabe: | 1. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XVII, 485 S. Ill., graph. Darst. |
| ISBN: | 019969933X 9780199699339 0199699321 9780199699322 |
Internformat
MARC
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| 007 | t | ||
| 008 | 140324s2014 ad|| |||| 00||| eng d | ||
| 020 | |a 019969933X |9 0-19-969933-X | ||
| 020 | |a 9780199699339 |c pbk |9 978-0-19-969933-9 | ||
| 020 | |a 0199699321 |9 0-19-969932-1 | ||
| 020 | |a 9780199699322 |c hbk |9 978-0-19-969932-2 | ||
| 020 | |a 9780199699339 |c pbk |9 978-0-19-969933-9 | ||
| 035 | |a (OCoLC)881299463 | ||
| 035 | |a (DE-599)BVBBV041751352 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-20 |a DE-706 |a DE-91 |a DE-703 |a DE-11 |a DE-19 |a DE-188 |a DE-384 |a DE-91G |a DE-29T | ||
| 082 | 0 | |a 530.143 |2 23 | |
| 084 | |a UO 4000 |0 (DE-625)146237: |2 rvk | ||
| 084 | |a PHY 023f |2 stub | ||
| 100 | 1 | |a Lancaster, Tom |e Verfasser |0 (DE-588)1050832337 |4 aut | |
| 245 | 1 | 0 | |a Quantum field theory for the gifted amateur |c Tom Lancaster ; Stephen J. Blundell |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2014 | |
| 300 | |a XVII, 485 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 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 | |
| 700 | 1 | |a Blundell, Stephen |d 1967- |e Verfasser |0 (DE-588)132321440 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027197723&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027197723 | ||
Datensatz im Suchindex
| _version_ | 1804152049595580416 |
|---|---|
| adam_text | Contents
0
Overture
1
0.1
What is quantum field theory?
1
0.2
What is a field?
2
0.3
Who is this book for?
2
0.4
Special relativity
3
0.5
Fourier transforms
б
0.6
Electromagnetism
7
I The Universe as a set of harmonic oscillators
9
1
Lagrangians
10
1.1
Fermat s principle
10
1.2
Newton s laws
10
1.3
Functionals
11
1.4
Lagrangians and least action
14
1.5
Why does it work?
16
Exercises
17
2
Simple harmonic oscillators
19
2.1
Introduction
19
2.2
Mass on a spring
19
2.3
A trivial generalization
23
2.4
Phonons
25
Exercises
27
3
Occupation number representation
28
3.1
A particle in a box
28
3.2
Changing the notation
29
3.3
Replace state labels with operators
31
3.4
Indistinguishability and symmetry
31
3.5
The continuum limit
35
Exercises
36
4
Making second quantization work
37
4.1
Field operators
37
4.2
How to second quantize an operator
39
4.3
The kinetic energy and the tight-binding Hamiltonian
43
4.4
Two particles
^4
χ
ContenL·
4.5
The Hubbard model
46
Exercises
48
II Writing down Lagrangians
49
5
Continuous systems
50
5.1
Lagrangians and Hamiltonians
50
5.2
A charged particle in an electromagnetic field
52
5.3
Classical fields
54
5.4
Lagrangian and Hamiltonian density
55
Exercises
58
6
A first stab at relativistic quantum mechanics
59
6.1
The Klein-Gordon equation
59
6.2
Probability currents and densities
61
6.3
Feynman s interpretation of the negative energy states
61
6.4
No conclusions
63
Exercises
63
7
Examples of Lagrangians, or how to write down a theory
64
7.1
A massless scalar field
64
7.2
A massive scalar field
65
7.3
An external source
66
7.4
The
φ*
theory
67
7.5
Two scalar fields
67
7.6
The complex scalar field
68
Exercises
69
III The need for quantum fields
71
8
The passage of time
72
8.1
SchrÖdinger s
picture and the time-evolution operator
72
8.2
The
Heisenberg
picture
74
8.3
The death of single-particle quantum mechanics
75
8.4
Old quantum theory is dead; long live fields!
76
Exercises
78
9
Quantum mechanical transformations
79
9.1
Translations in spacetime
79
9.2
Rotations
82
9.3
Representations of transformations
83
9.4
Transformations of quantum fields
85
9.5
Lorentz
transformations
86
Exercises
88
10
Symmetry
90
10.1
Invariance
and conservation
90
Contents xi
10.2
Noether s theorem
92
10.3 Spacetime
translation
94
10.4
Other symmetries
96
Exercises
97
11
Canonical quantization of fields
98
11.1
The canonical quantization machine
98
11.2
Normalizing factors
101
11.3
What becomes of the Hamiltonian?
102
11.4
Normal ordering
104
11.5
The meaning of the mode expansion
106
Exercises
108
12
Examples of canonical quantization
109
12.1
Complex scalar field theory
109
12.2
Noether s current for complex scalar field theory 111
12.3
Complex scalar field theory in the non-relativistic limit
112
Exercises
116
13
Fields with many components and
massive electromagnet ism
117
13.1
Internal symmetries
117
13.2
Massive
electromagnetism
120
13.3
Polarizations and projections
123
Exercises
125
14
Gauge fields and gauge theory
126
14.1
What is a gauge field?
126
14.2
Electromagnetism
is the simplest gauge theory
129
14.3
Canonical quantization of the electromagnetic field
131
Exercises
134
15
Discrete transformations
135
15.1
Charge conjugation
135
15.2
Parity
136
15.3
Time reversal
137
15.4
Combinations of discrete and continuous transformations
139
Exercises
142
IV Propagators and perturbations
143
16
Propagators and Green s functions
144
16.1
What is a Green s function?
144
16.2
Propagators in quantum mechanics
146
16.3
Turning it around: quantum mechanics from the
propagator and a first look at perturbation theory
149
16.4
The many faces of the propagator
151
Exercises
152
xii Contents
17
Propagators and fields
154
17.1
The field propagator in outline
155
17.2
The Feynman propagator
156
17.3
Finding the free propagator for scalar field theory
158
17.4
Yukawa s force-carrying particles
159
17.5
Anatomy of the propagator
162
Exercises
163
18
The S-matrix
165
18.1
The ¿ -matrix: a hero for our times
166
18.2
Some new machinery: the interaction representation
167
18.3
The interaction picture applied to scattering
168
18.4
Perturbation expansion of the S-matrix
169
18.5
Wick s theorem
171
Exercises
174
19
Expanding the S-matrix: Feynman diagrams
175
19.1
Meet some interactions
176
19.2
The example of
φ4
theory
177
19.3
Anatomy of a diagram
181
19.4
Symmetry factors
182
19.5
Calculations in p-space
183
19.6
A first look at scattering
186
Exercises
187
20
Scattering theory
188
20.1
Another theory. Yukawa s
ψ^φφ
interactions
188
20.2
Scattering in the
ψϊψφ
theory
190
20.3
The transition matrix and the invariant amplitude
192
20.4
The scattering cross-section
193
Exercises
194
V Interlude: wisdom from statistical physics
195
21
Statistical physics: a crash course
196
21.1
Statistical mechanics in a nutshell
196
21.2
Sources in statistical physics
197
21.3
A look ahead
198
Exercises
199
22
The generating functional for fields
201
22.1
How to find Green s functions
201
22.2
Linking things up with the Gell-Marm-Low theorem
203
22.3
How to calculate Green s functions with diagrams
204
22.4
More facts about diagrams
206
Exercises
208
Contents xiii
VI Path integrals
209
23
Path integrals: I said to him, You re crazy
210
23.1
How to do quantum mechanics using path integrals
210
23.2
The Gaussian integral
213
23.3
The propagator for the simple harmonic oscillator
217
Exercises
220
24
Field integrals
221
24.1
The functional integral for fields
221
24.2
Which field integrals should you do?
222
24.3
The generating functional for scalar fields
223
Exercises
226
25
Statistical field theory
228
25.1
Wick rotation and Euclidean space
229
25.2
The partition function
231
25.3
Perturbation theory and Feynman rules
233
Exercises
236
26
Broken symmetry
237
26.1
Landau theory
237
26.2
Breaking symmetry with a Lagrangian
239
26.3
Breaking a continuous symmetry:
Goldstone
modes
240
26.4
Breaking a symmetry in a gauge theory
242
26.5
Order in reduced dimensions
244
Exercises
245
27
Coherent states
247
27.1
Coherent states of the harmonic oscillator
247
27.2
What do coherent states look like?
249
27.3
Number, phase and the phase operator
250
27.4
Examples of coherent states
252
Exercises
253
28 Grassmann
numbers: coherent states
and the path integral for
fermions
255
28.1
Grassmarm numbers
255
28.2
Coherent states for
fermions
257
28.3
The path integral for
fermions
257
Exercises
258
VII Topological
ideas
259
29
Topological objects
260
29.1 WЪat
is topology?
260
29.2
Kinks
262
29.3
Vortices
264
Exercises
266
xiv Contents
30
Topologica!
field theory
267
30.1
Fractional statistics
à la
Wilczek:
the strange case of anyons
267
30.2
Chern-Simons theory
269
30.3
Fractional statistics from Chern-Simons theory
271
Exercises
272
VIII
Renormalization: taming the infinite
273
31
Renormalization, quasiparticles and the Fermi surface
274
31.1
Recap: interacting and non-interacting theories
274
31.2
Quasiparticles
276
31.3
The propagator for a dressed particle
277
31.4
Elementary quasiparticles in a metal
279
31.5
The Landau Fermi liquid
280
Exercises
284
32
Renormalization: the problem and its solution
285
32.1
The problem is divergences
285
32.2
The solution is counterterms
287
32.3
How to tame an integral
288
32.4
What counterterms mean
290
32.5
Making renormalization even simpler
292
32.6
Which theories are renormalizable?
293
Exercises
294
33
Renormalization in action:
propagators and Feynman diagrams
295
33.1
How interactions change the propagator in perturbation
theory
295
33.2
The role of counterterms: renormalization conditions
297
33.3
The vertex function
298
Exercises
300
34
The renormalization group
302
34.1
The problem
302
34.2
Flows in parameter space
304
34.3
The renormalization group method
305
34.4
Application
1:
asymptotic freedom
307
34.5
Application
2:
Anderson localization
308
34.6
Application
3:
the Kosterlitz-Thouless transition
309
Exercises
312
35
Ferromagnetism: a renormalization group tutorial
313
35.1
Background: critical phenomena and scaling
313
35.2
The ferromagnetic transition and critical phenomena
315
Exercises
320
Contents xv
IX Putting a spin on QFT
321
36
The Dirac equation
322
36.1
The Dirac equation
322
36.2
Massless particles: left- and right-handed wave functions
323
36.3
Dirac and Weyl spinors
327
36.4
Basis states for superpositions
330
36.5
The non-relativistic limit of the Dirac equation
332
Exercises
334
37
How to transform a spinor
336
37.1
Spinors aren t vectors
336
37.2
Rotating spinors
337
37.3
Boosting spinors
337
37.4
Why are there four components in the Dirac equation?
339
Exercises
340
38
The quantum Dirac field
341
38.1
Canonical quantization and Noether current
341
38.2
The fermion propagator
343
38.3
Feynman rules and scattering
345
38.4
Local symmetry and a gauge theory for
fermions
346
Exercises
347
39
A rough guide to quantum electrodynamics
348
39.1
Quantum light and the photon propagator
348
39.2
Feynman rules and a first QED process
349
39.3
Gauge
invariance
in QED
351
Exercises
353
40
QED scattering: three famous cross-sections
355
40.1
Example
1:
Rutherford scattering
355
40.2
Example
2:
Spin sums and the
Mott
formula
356
40.3
Example
3:
Compton scattering
357
40.4
Crossing symmetry
358
Exercises
359
41
The renormalization of QED and two great results
360
41.1
Renormalizing the photon propagator: dielectric vacuum
361
41.2
The renormalization group and the electric charge
364
41.3
Vertex corrections and the electron ^-factor
365
Exercises
368
X Some applications from the world
of condensed matter
369
42
Superfluide
370
42.1
Bogoliubov s hunting license
370
xvi
Contents
42.2
Bogoliubov s transformation
372
42.3
Superfluide
and fields
374
42.4
The current in a superfluid
377
Exercises
379
43
The many-body problem and the metal
380
43.1
Mean-field theory
380
43.2
The Hartree-Fock ground state energy of a metal
383
43.3
Excitations in the mean-field approximation
386
43.4
Electrons and holes
388
43.5
Finding the excitations with propagators
389
43.6
Ground states and excitations
390
43.7
The random phase approximation
393
Exercises
398
44
Superconductors
400
44.1
A model of a superconductor
400
44.2
The ground state is made of Cooper pairs
402
44.3
Ground state energy
403
44.4
The quasiparticles are
bogolons
405
44.5
Broken symmetry
406
44.6
Field theory of a charged superfluid
407
Exercises
409
45
The fractional quantum Hall fluid
411
45.1
Magnetic translations
411
45.2
Landau Levels
413
45.3
The integer quantum Hall effect
415
45.4
The fractional quantum Hall effect
417
Exercises
421
XI Some applications from the world
of particle physics
423
46
Non-abelian gauge theory
424
46.1
Abelian gauge theory revisited
424
46.2
Yang-Mills theory
425
46.3
Interactions and dynamics of
W»
428
46.4
Breaking symmetry with a non-abelian gauge theory
430
Exercises
432
47
The Weinberg-Salam model
433
47.1
The symmetries of Nature before symmetry breaking
434
47.2
Introducing the Higgs field
437
47.3
Symmetry breaking the Higgs field
438
47.4
The origin of electron mass
439
47.5
The photon and the gauge bosons
440
Exercises
443
Contents xvii
48 Majorana
fermions
444
48.1
The
Majorana
solution
444
48.2
Field operators
446
48.3
Majorana
mass and charge
447
Exercises
450
49
Magnetic
monopoles
451
49.1
Dirac s
monopole
and the Dirac string
451
49.2
The t Hooft-Polyakov
monopole
453
Exercises
456
50
Instantons,
tunnelling and the end of the world
457
50.1 Instantons in
quantum particle mechanics
458
50.2
A particle in a potential well
459
50.3
A particle in a double well
460
50.4
The fate of the false vacuum
463
Exercises
466
A Further reading
467
В
Useful complex analysis
473
B.I What is an analytic function?
473
B.2 What is a pole?
474
B.3 How to find a residue
474
B.4 Three rules of contour integrals
475
B.5 What is a branch cut?
477
B.6 The principal value of an integral
478
Index
480
|
| any_adam_object | 1 |
| author | Lancaster, Tom Blundell, Stephen 1967- |
| author_GND | (DE-588)1050832337 (DE-588)132321440 |
| author_facet | Lancaster, Tom Blundell, Stephen 1967- |
| author_role | aut aut |
| author_sort | Lancaster, Tom |
| author_variant | t l tl s b sb |
| building | Verbundindex |
| bvnumber | BV041751352 |
| classification_rvk | UO 4000 |
| classification_tum | PHY 023f |
| ctrlnum | (OCoLC)881299463 (DE-599)BVBBV041751352 |
| 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 |
| edition | 1. ed. |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV041751352 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:04:32Z |
| institution | BVB |
| isbn | 019969933X 9780199699339 0199699321 9780199699322 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027197723 |
| oclc_num | 881299463 |
| open_access_boolean | |
| owner | DE-20 DE-706 DE-91 DE-BY-TUM DE-703 DE-11 DE-19 DE-BY-UBM DE-188 DE-384 DE-91G DE-BY-TUM DE-29T |
| owner_facet | DE-20 DE-706 DE-91 DE-BY-TUM DE-703 DE-11 DE-19 DE-BY-UBM DE-188 DE-384 DE-91G DE-BY-TUM DE-29T |
| physical | XVII, 485 S. Ill., graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Lancaster, Tom Verfasser (DE-588)1050832337 aut Quantum field theory for the gifted amateur Tom Lancaster ; Stephen J. Blundell 1. ed. Oxford [u.a.] Oxford Univ. Press 2014 XVII, 485 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Quantenfeldtheorie (DE-588)4047984-5 s DE-604 Blundell, Stephen 1967- Verfasser (DE-588)132321440 aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027197723&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lancaster, Tom Blundell, Stephen 1967- Quantum field theory for the gifted amateur Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4123623-3 |
| title | Quantum field theory for the gifted amateur |
| title_auth | Quantum field theory for the gifted amateur |
| title_exact_search | Quantum field theory for the gifted amateur |
| title_full | Quantum field theory for the gifted amateur Tom Lancaster ; Stephen J. Blundell |
| title_fullStr | Quantum field theory for the gifted amateur Tom Lancaster ; Stephen J. Blundell |
| title_full_unstemmed | Quantum field theory for the gifted amateur Tom Lancaster ; Stephen J. Blundell |
| title_short | Quantum field theory for the gifted amateur |
| title_sort | quantum field theory for the gifted amateur |
| 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=027197723&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lancastertom quantumfieldtheoryforthegiftedamateur AT blundellstephen quantumfieldtheoryforthegiftedamateur |