Boulevard of broken symmetries: effective field theories of condensed matter
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2008
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXII, 390 S. |
| ISBN: | 9789812813909 |
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MARC
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| 100 | 1 | |a Schakel, Adriaan M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Boulevard of broken symmetries |b effective field theories of condensed matter |c Adriaan M. J. Schakel |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2008 | |
| 300 | |a XXII, 390 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Condensed matter | |
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Record in the Search Index
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| adam_text | Contents
Preface
vii
Synopsis xi
Notation and Conventions xv
1.
Classical Field Theory
1
1.1
One-Dimensional Crystal
.................... 1
1.2
Action Principle
........................ 2
1.3
Noether s Theorem
....................... 3
1.4
Nonrelativistic Field Theory
.................. 7
1.5
Spontaneously Broken Symmetries
.............. 11
1.6
Effective Theory of Hydrodynamics
.............. 14
1.7
SoundWaves
.......................... 16
1.8
Topological Defects
...................... 19
1.9
Homotopy Groups
....................... 21
1.10
Quantized Vortices
....................... 26
1.11
Villain Vector Potential
.................... 27
2.
Quantum Field Theory
31
2.1
Quantum Statistical Mechanics
................ 31
2.2
Finite-Temperature Field Theory
............... 36
2.3
Functional Integrals
...................... 38
2.4
Feynman Propagator
...................... 42
2.5
Feynman Diagrams
....................... 47
2.6
Connected Green Functions
.................. 53
2.7
Effective Action
........................ 55
xx Contents
2.8 Linear
Response
Theory
.................... 59
2.9 Ward
Identities
......................... 64
3.
Calculation
Tools 67
3.1
Derivative Expansion
...................... 67
3.2
Free Electron Gas in an External Magnetic Field
....... 69
3.3 Goldstone-
Wilczek
Currents
.................. 71
3.4
Optical Phonons
........................ 75
3.5
Geometric Phase
........................ 77
3.6
Monopole
Action
........................ 81
3.7
Wess-Zumino Terms
...................... 84
3.8
Landau-Levels Technique
................... 86
3.9
Magnetic Susceptibility of an Electron Gas
.......... 91
4.
Bose-Einstein Condensation
95
4.1
Ideal
Bose
Gas
......................... 95
4.2
Critical Properties
........................ 97
4.3
Ideal
Bose
Gas in a Harmonic Trap
.............. 100
4.4
Gross-Pitaevskii Theory
.................... 102
4.5
Bogoliubov Theory
....................... 104
4.6
Renormalization
........................ 106
4.7
One-Loop Corrections
..................... 110
4.8
Phonon Decay
......................... 114
4.9
Effective Theory
........................ 115
4.10
Finite Temperature
....................... 120
4.11
Large-A Expansion
....................... 128
4.12
Two-Fluid Model
........................ 132
4.13
Impurities
........................... 136
4.14
Bose-Hubbard Model
..................... 138
5.
Vortices in 2D
147
5.1
Vortex Dynamics
........................ 147
5.2
2D Coulomb Gas
........................ 153
5.3
Berezinskii-Kosterlitz-Thouless Transition
.......... 155
5.4
Sine-Gordon Model
...................... 159
5.5
Superfluid 4He Films
...................... 163
5.6
Duality
............................. 165
Contents
ххј
6.
Fermi
Gases 169
6.1
Interacting
Fermi Gas
.....................169
6.2
Impurities
...........................172
6.3
Conductivity
..........................175
6.4
Kondo Effect
..........................179
6.5
Degenerate Electron Gas
....................183
6.6
Thermodynamic Potential
...................190
6.7
Self-Energy
...........................194
7.
Magnetic Order in Fermi Systems
197
7.1
Hubbard Model
.........................197
7.2
Ferromagnetic State
.......................201
7.3
Ferromagnetic Spin Waves
...................203
7.4
Antiferromagnetic State
....................207
7.5
Antiferromagnetic Spin Waves
.................210
8.
Superconductivity
213
8.1
BCS Theory
..........................213
8.2
Gap Equation
..........................214
8.3
Anderson-Bogoliubov Mode
..................218
8.4
Linear Response
........................221
8.5
Flux Quantization
........................223
8.6
Plasma Mode
..........................224
8.7
Josephson
Effect
........................225
8.8
Effective Potential
.......................227
8.9
Effective Action
.........................228
8.10
Ginzburg-Landau Theory
...................229
8.11
Condensation Energy
.....................234
8.12
Ginzburg Region
........................236
8.13
Magnetic Vortices
........................238
8.14
Mixed State
...........................243
8.15
Gapless Superconductivity
...................246
9.
Duality
253
9.1
Superconducting Films
.....................253
9.2
Bosonization
..........................259
9.3
Chiral Anomaly
.........................263
9.4
Fermion Condensate
......................265
xxii Contents
9.5 Index Theorem......................... 268
9.6
Ô
Vacuum............................
271
9.7 Massive Schwinger Model................... 275
9.8 Peierls
Instability
........................ 277
9.9
Fractional
Charge........................ 281
10.
From BCS to
ВЕС
285
10.1
Composite Boson Limit
.................... 285
10.2
Ultracold Fermi Gases
..................... 288
10.3
Derivative Expansion
...................... 289
10.4
Quantum Phase Transitions
................... 292
10.5
Superconductor-Insulator Transition
.............. 294
11.
Superfluidi
299
11.1
P-State
Triplet Pairing
..................... 299
11.2
Phase Diagram
......................... 304
11.3
Fermionic Excitations
..................... 307
11.4
Boojums
............................ 310
11.5
Callan-Harvey Effect
...................... 313
11.6
Wess-Zumino Term
....................... 318
11.7
Topological Defects
....................... 321
12.
Quantum Hall Effect
327
12.1
2D Electron Gas in a Strong Magnetic Field
......... 328
12.2
Many-Particle Wave Function
................. 331
12.3
Fluxons
............................. 335
12.4
IQHE
.............................. 338
12.5
Laughlin Wave Function
.................... 340
12.6
Composite
Fermions
...................... 341
12.7
Fractional Charge
........................ 343
12.8
Near
v
= 1/2.......................... 344
12.9
Aharonov-Bohm Effect
.................... 346
12.10
Chern-Simons Theory
..................... 347
12.11
Graphene
............................ 350
Bibliography
357
Author Index
373
Index
379
|
| adam_txt |
Contents
Preface
vii
Synopsis xi
Notation and Conventions xv
1.
Classical Field Theory
1
1.1
One-Dimensional Crystal
. 1
1.2
Action Principle
. 2
1.3
Noether's Theorem
. 3
1.4
Nonrelativistic Field Theory
. 7
1.5
Spontaneously Broken Symmetries
. 11
1.6
Effective Theory of Hydrodynamics
. 14
1.7
SoundWaves
. 16
1.8
Topological Defects
. 19
1.9
Homotopy Groups
. 21
1.10
Quantized Vortices
. 26
1.11
Villain Vector Potential
. 27
2.
Quantum Field Theory
31
2.1
Quantum Statistical Mechanics
. 31
2.2
Finite-Temperature Field Theory
. 36
2.3
Functional Integrals
. 38
2.4
Feynman Propagator
. 42
2.5
Feynman Diagrams
. 47
2.6
Connected Green Functions
. 53
2.7
Effective Action
. 55
xx Contents
2.8 Linear
Response
Theory
. 59
2.9 Ward
Identities
. 64
3.
Calculation
Tools 67
3.1
Derivative Expansion
. 67
3.2
Free Electron Gas in an External Magnetic Field
. 69
3.3 Goldstone-
Wilczek
Currents
. 71
3.4
Optical Phonons
. 75
3.5
Geometric Phase
. 77
3.6
Monopole
Action
. 81
3.7
Wess-Zumino Terms
. 84
3.8
Landau-Levels Technique
. 86
3.9
Magnetic Susceptibility of an Electron Gas
. 91
4.
Bose-Einstein Condensation
95
4.1
Ideal
Bose
Gas
. 95
4.2
Critical Properties
. 97
4.3
Ideal
Bose
Gas in a Harmonic Trap
. 100
4.4
Gross-Pitaevskii Theory
. 102
4.5
Bogoliubov Theory
. 104
4.6
Renormalization
. 106
4.7
One-Loop Corrections
. 110
4.8
Phonon Decay
. 114
4.9
Effective Theory
. 115
4.10
Finite Temperature
. 120
4.11
Large-A'Expansion
. 128
4.12
Two-Fluid Model
. 132
4.13
Impurities
. 136
4.14
Bose-Hubbard Model
. 138
5.
Vortices in 2D
147
5.1
Vortex Dynamics
. 147
5.2
2D Coulomb Gas
. 153
5.3
Berezinskii-Kosterlitz-Thouless Transition
. 155
5.4
Sine-Gordon Model
. 159
5.5
Superfluid 4He Films
. 163
5.6
Duality
. 165
Contents
ххј
6.
Fermi
Gases 169
6.1
Interacting
Fermi Gas
.169
6.2
Impurities
.172
6.3
Conductivity
.175
6.4
Kondo Effect
.179
6.5
Degenerate Electron Gas
.183
6.6
Thermodynamic Potential
.190
6.7
Self-Energy
.194
7.
Magnetic Order in Fermi Systems
197
7.1
Hubbard Model
.197
7.2
Ferromagnetic State
.201
7.3
Ferromagnetic Spin Waves
.203
7.4
Antiferromagnetic State
.207
7.5
Antiferromagnetic Spin Waves
.210
8.
Superconductivity
213
8.1
BCS Theory
.213
8.2
Gap Equation
.214
8.3
Anderson-Bogoliubov Mode
.218
8.4
Linear Response
.221
8.5
Flux Quantization
.223
8.6
Plasma Mode
.224
8.7
Josephson
Effect
.225
8.8
Effective Potential
.227
8.9
Effective Action
.228
8.10
Ginzburg-Landau Theory
.229
8.11
Condensation Energy
.234
8.12
Ginzburg Region
.236
8.13
Magnetic Vortices
.238
8.14
Mixed State
.243
8.15
Gapless Superconductivity
.246
9.
Duality
253
9.1
Superconducting Films
.253
9.2
Bosonization
.259
9.3
Chiral Anomaly
.263
9.4
Fermion Condensate
.265
xxii Contents
9.5 Index Theorem. 268
9.6
Ô
Vacuum.
271
9.7 Massive Schwinger Model. 275
9.8 Peierls
Instability
. 277
9.9
Fractional
Charge. 281
10.
From BCS to
ВЕС
285
10.1
Composite Boson Limit
. 285
10.2
Ultracold Fermi Gases
. 288
10.3
Derivative Expansion
. 289
10.4
Quantum Phase Transitions
. 292
10.5
Superconductor-Insulator Transition
. 294
11.
Superfluidi
299
11.1
P-State
Triplet Pairing
. 299
11.2
Phase Diagram
. 304
11.3
Fermionic Excitations
. 307
11.4
Boojums
. 310
11.5
Callan-Harvey Effect
. 313
11.6
Wess-Zumino Term
. 318
11.7
Topological Defects
. 321
12.
Quantum Hall Effect
327
12.1
2D Electron Gas in a Strong Magnetic Field
. 328
12.2
Many-Particle Wave Function
. 331
12.3
Fluxons
. 335
12.4
IQHE
. 338
12.5
Laughlin Wave Function
. 340
12.6
Composite
Fermions
. 341
12.7
Fractional Charge
. 343
12.8
Near
v
= 1/2. 344
12.9
Aharonov-Bohm Effect
. 346
12.10
Chern-Simons Theory
. 347
12.11
Graphene
. 350
Bibliography
357
Author Index
373
Index
379 |
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| id | DE-604.BV023307759 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T20:49:10Z |
| indexdate | 2024-07-09T21:15:30Z |
| institution | BVB |
| isbn | 9789812813909 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016492093 |
| oclc_num | 600867627 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-703 DE-29T DE-91G DE-BY-TUM DE-11 DE-20 |
| owner_facet | DE-19 DE-BY-UBM DE-703 DE-29T DE-91G DE-BY-TUM DE-11 DE-20 |
| physical | XXII, 390 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Schakel, Adriaan M. Verfasser aut Boulevard of broken symmetries effective field theories of condensed matter Adriaan M. J. Schakel New Jersey [u.a.] World Scientific 2008 XXII, 390 S. txt rdacontent n rdamedia nc rdacarrier Condensed matter Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Effektive Theorie (DE-588)4560327-3 gnd rswk-swf Kondensierte Materie (DE-588)4132810-3 gnd rswk-swf Kondensierte Materie (DE-588)4132810-3 s Quantenfeldtheorie (DE-588)4047984-5 s Effektive Theorie (DE-588)4560327-3 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=016492093&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schakel, Adriaan M. Boulevard of broken symmetries effective field theories of condensed matter Condensed matter Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd Effektive Theorie (DE-588)4560327-3 gnd Kondensierte Materie (DE-588)4132810-3 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4560327-3 (DE-588)4132810-3 |
| title | Boulevard of broken symmetries effective field theories of condensed matter |
| title_auth | Boulevard of broken symmetries effective field theories of condensed matter |
| title_exact_search | Boulevard of broken symmetries effective field theories of condensed matter |
| title_exact_search_txtP | Boulevard of broken symmetries effective field theories of condensed matter |
| title_full | Boulevard of broken symmetries effective field theories of condensed matter Adriaan M. J. Schakel |
| title_fullStr | Boulevard of broken symmetries effective field theories of condensed matter Adriaan M. J. Schakel |
| title_full_unstemmed | Boulevard of broken symmetries effective field theories of condensed matter Adriaan M. J. Schakel |
| title_short | Boulevard of broken symmetries |
| title_sort | boulevard of broken symmetries effective field theories of condensed matter |
| title_sub | effective field theories of condensed matter |
| topic | Condensed matter Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd Effektive Theorie (DE-588)4560327-3 gnd Kondensierte Materie (DE-588)4132810-3 gnd |
| topic_facet | Condensed matter Quantum field theory Quantenfeldtheorie Effektive Theorie Kondensierte Materie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016492093&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schakeladriaanm boulevardofbrokensymmetrieseffectivefieldtheoriesofcondensedmatter |