Thermal quantum field theory: algebraic aspects and applications
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| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2009
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 461 S. graph. Darst. |
| ISBN: | 9812818871 9789812818874 |
Internformat
MARC
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| 084 | |a PHY 023f |2 stub | ||
| 245 | 1 | 0 | |a Thermal quantum field theory |b algebraic aspects and applications |c Faqir C. Khanna ... |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2009 | |
| 300 | |a XIX, 461 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Endliche Temperatur |0 (DE-588)4736704-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Symmetrie |0 (DE-588)4058724-1 |2 gnd |9 rswk-swf |
| 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 | 1 | |a Endliche Temperatur |0 (DE-588)4736704-0 |D s |
| 689 | 0 | 2 | |a Symmetrie |0 (DE-588)4058724-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Khanna, Faqir C. |e Sonstige |4 oth | |
| 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=018010203&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018010203 | ||
Datensatz im Suchindex
| _version_ | 1804140015327903744 |
|---|---|
| adam_text | Contents
Preface
VII
Part I
—
General Principles
1
1.
Elements of Thermodynamics
3
1.1
Kinematical aspects of thermal physics
............... 4
1.2
Dynamical aspects of thermal physics
................ 6
1.3
Equations of state
........................... 7
1.4
The meaning of intensive variables
................. 9
1.5
Thermodynamical potentials
..................... 12
1.6
Gibbs-Duhem relation
........................ 15
1.7
Second derivatives
........................... 16
1.8
Example: ideal gas and generalizations
............... 19
1.8.1
State equation for an ideal gas
............... 19
1.8.2
The van
der Waals
equation
................. 20
1.9
Stability conditions and phase transitions
............. 21
2.
Elements of Statistical Mechanics
27
2.1
Macro- and micro-physics
...................... 27
2.2
Liouville-von Neumann equation
................... 29
2.3
Gibbs ensembles
............................ 31
2.3.1
Micro-canonical ensemble
.................. 31
2.3.2
Canonical ensemble
..................... 32
2.3.3
Grand-canonical ensemble
.................. 33
2.3.4
Equivalence among the ensembles
............. 34
2.4
Wigner function formalism
...................... 35
3.
Partition Function and Path Integral
39
3.1
Partition function and the propagator
................ 39
xiv
Thermal Quantum Field Theory: Algebraic Aspects and Applications
3.2
Path integral in quantum mechanics
................. 42
3.3
Classical fields
............................. 43
3.4
Canonical quantization of scalar fields
................ 46
3.5
Path integral for a scalar field
.................... 48
3.6
Canonical quantization of the Dirac field
.............. 51
3.7
Path integral for the Dirac field
................... 55
4.
Zero Temperature Interacting Fields
59
4.1
Generating functional for bosons
................... 59
4.1.1
Feynman rules in momentum space
............. 62
4.2
The effective action
.......................... 63
4.3
Gauge fields
.............................. 66
4.4
Generating functional for gauge fields
................ 70
4.5
U(l) gauge theory
........................... 73
4.6
St/(3) gauge theory
.......................... 74
4.7
Scattering amplitudes
......................... 77
4.8
S-matrix in the canonical approach
................. 85
Part II
—
Thermal Fields
87
5.
Thermofield Dynamics: Kinematical Symmetry Algebraic Basis
89
5.1
Thermal Hilbert space
........................ 91
5.2
The meaning of the doubling: thermo-algebras
........... 93
5.2.1
Generators of symmetry and
observables
.......... 93
5.2.2
Doubled Lie algebra
..................... 94
5.2.3
Tilde conjugation rules
................... 96
5.3
Tilde and non-tilde operators
.................... 97
5.4
Liouville-von Neumann equation
................... 100
5.5
Physical implications of thermo-algebras
.............. 102
6.
Thermal Oscillators: Bosons and
Fermions
105
6.1
Boson oscillators
............................ 105
6.1.1
Thermal vacuum
....................... 106
6.1.2
Bogoliubov transformation
................. 107
6.1.3
Thermal operators
...................... 108
6.1.4
Matrix notation
.......................
Ill
6.2
Fermion oscillators
.......................... 112
6.2.1
Thermal vacuum
....................... 112
6.2.2
Bogoliubov transformation
................. 113
6.2.3
Thermal operators
...................... 114
6.2.4
Matrix notation
....................... 115
Contents xv
6.3 TFD
and spin
1/2
lattices......................
116
6.3.1
Boson representation for the SU(2) algebra
........ 117
6.3.2
Thermo-5ř7(2)
algebra
.................... 118
7.
Thermal
Poincaré
and Galilei Groups
121
7.1
The
Poincaré
group
.......................... 121
7.2
Relativistic density matrices
..................... 122
7.2.1
Bosons
............................. 124
7.2.2
Fermions
........................... 125
7.3
The Galilei group
........................... 126
7.4
Galilean density matrices
....................... 128
7.5
Lagrangians
.............................. 131
8.
Thermal Propagator
133
8.1
Thermal Klein-Gordon field
..................... 133
8.2
Thermal Dirac field
.......................... 139
8.3
Doubled notation for bosons
..................... 142
8.4
Generating functional for bosons
................... 143
8.5
Generating functional for
fermions
.................. 145
8.6
Thermal gauge fields
......................... 146
9.
Scattering Process at Finite Temperature
149
9.1
Scattering matrix in TFD
...................... 150
9.2
Reaction rates
............................. 152
9.3
Decay of particles and generalized Cutkosky rules
......... 153
9.4
Decay of Higgs meson
......................... 156
9.5
The detailed balance
......................... 157
9.6
Scattering cross-section of
1 + 2 -> 1 + 2 ............. 158
9.6.1
Boson-boson scattering
................... 158
9.6.2
Fermion-fermion scattering
................. 158
9.7
Fermion-boson scattering
....................... 159
10.
Topics on Renormalization Theory
161
10.1
Ultraviolet divergences
........................ 161
10.2
Regularization
............................. 164
10.3
Renormalization
............................ 165
10.3.1
Renormalization parts in the
λι^4
theory
.......... 171
10.3.2
The Callan-Zimanzik equation
............... 172
10.4
Bogoliubov recurrence
........................ 173
10.4.1
Dimensional renormalization
................ 175
10.4.2
Other renormalization procedures
............. 177
10.4.3
Borei
summability
...................... 179
xvi
Thermal Quantum
Field Theory: Algebraic Aspects and Applications
10.5
Temperature effects
..........................179
11.
Ward-Takahashi Relations and Gauge Symmetry
183
11.1
Ward relation
.............................184
11.2
Ward-Takahashi relations
.......................184
11.3
Applications of generalized Ward-Takahashi relations
.......186
11.3.1
W
-Т
relations for the case of
η
-body
current
amplitudes
.......................... 186
11.3.2
Ward-Takahashi relations at finite temperature
...... 188
11.4
Transverse Ward-Takahashi relations
................ 191
11.5
Transverse
W
-Т
relation in momentum space
........... 194
11.5.1
Pull vertex for the fermion-gauge boson vertex
...... 195
11.5.2 Tranverse
W
-Т
relation for axial current
.......... 196
11.5.3
Transverse
W
-Т
relation at finite temperature
...... 196
11.6
W
-Т
relations and spontaneous symmetry breaking
........ 196
Part III
—
Applications to Quantum Optics
199
12.
Thermalized States of a Field Mode
201
12.1
Thermalized states
..........................201
12.1.1
Thermal number states
................... 202
12.1.2
Thermal coherent states
................... 202
12.1.3
Thermal displaced number states
.............. 204
12.1.4
Thermal squeezed states
................... 205
12.2
Physical interpretation
........................ 207
12.3
Other possibilities of thermalized states
............... 213
12.3.1
Thermal tilde states
.....................213
12.3.2
Physical meaning of the thermal tilde states
.......215
12.3.3
General states of WT
.....................217
13.
Nonclassical Properties of Thermal Quantum States
221
13.1
Photon statistics
...........................221
13.1.1
Thermal states
........................ 222
13.1.2
Thermal tilde states
..................... 227
13.2
Quadrature squeezing
......................... 228
13.3
Atomic population inversion
..................... 231
13.4
Phase space representation
...................... 237
13.4.1
Q-function of the thermal number state
..........238
13.4.2
Wigner function of the thermal number state
.......239
13.4.3
ñ-representation
and nonclassical depth of the
thermal number state
....................240
Contents xvii
13.4.4 Phase
space representations of the thermal tilde number
state
..............................241
14.
SU
(2)
and
SU
(1,
1)
Systems: Entanglement
245
14.1
Maximum entanglement
....................... 245
14.2
Maximally entangled states and
517(1,1)
symmetry
........ 247
14.3
Maximally entangled states and SU(2) symmetry
......... 249
14.4
Entanglement of a system with fixed spin
.............. 250
14.5
Entanglement of two-boson squeezed states
............. 252
14.6
Coherent fermion states and density matrix operators
....... 255
14.7
Entanglement of two-mode squeezed fermion states
........ 258
Part IV
—
Compactifled Fields
261
15.
Compactified Fields
263
15.1
Compactification and topology
....................264
15.1.1
Compactification of one space dimension
.......... 264
15.1.2
Compactification of time dimension
............ 268
15.1.3
Compactification of space and time
............. 269
15.1.4
Compactification in
eř-dimensions
.............. 271
15.2
Generalized Bogoliubov transformation
............... 272
15.3
Field theory
.............................. 274
15.4
Feynman rules
............................. 277
16.
Casimir
Effect for the Electromagnetic Field
279
16.1
The vacuum state of the electromagnetic field
...........280
16.2
The
Casimir
effect
...........................287
16.2.1
Casimir
effect at zero temperature
.............287
16.2.2
Casimir
effect at non-zero temperature
...........288
16.3
Casimir-Boyer model
.........................290
17.
Casimir
Effect for
Fermions
293
17.1
Casimir
effect in T
.......................... 294
17.2
Compactification in higher dimensions
............... 296
17.3
Casimir
effect for two plates
..................... 298
17.4 Casimir
effect for a waveguide
.................... 299
17.5 Casimir
effect for a box
........................ 303
17.6 Casimir
effect for a non-interacting massless QCD
......... 306
18.
Compactified
λψ4
Theory
311
18.1
Compactification of a d-dimensional subspace
...........311
xviii
Thermal Quantum Field Theory: Algebraic Aspects and Applications
18.2
Subtraction scheme
..........................314
18.3
The zero-temperature compactified model
.............317
18.3.1
Wick-ordered model
..................... 317
18.3.2
The model without Wick-ordering
............. 317
18.4
The compactified model at finite temperature: spontaneous
symmetry breaking
.......................... 322
18.4.1
Mass behavior and critical curve
.............. 323
19.
Phase Transitions in Confined Systems: Application to Super¬
conducting Films
327
19.1
Overview
................................327
19.2
Second-order phase transition in superconducting films
......329
19.2.1
The effective potential for the Ginzburg-Landau
model with one compactified dimension
.......... 330
19.3
Mass renormalization and transition temperature
......... 333
19.3.1
Effect of the coupling-constant correction on TC(L)
.... 334
19.4
Critical behavior of
type
-П
superconducting films in
a magnetic field
............................337
19.4.1
Coupling-constant correction in the presence of an
external magnetic field
....................337
19.4.2
The gap equation and the critical curve
..........339
20.
Second-Order Phase Transition in Wires and Grains
343
20.1
Compactification of a d-dimensional subspace
........... 343
20.2
Critical behavior for wires
...................... 346
20.3
Critical behavioT for grains
...................... 349
20.4
Boundary effects on the coupling constant
............. 352
20.5
Effects of the boundary-corrected coupling constant on the
critical behavior
............................353
20.5.1
Effects of the boundary-corrected coupling constant
on the phase transition for wires
..............356
20.5.2
Effects of the boundary-corrected coupling constant
on the phase transition for grains
..............358
20.6
Universal behavior of size-effects in second-order phase
transitions
...............................361
21.
First-Order Phase Transitions in Confined Systems
365
21.1
Effective potential with compactification of a
d-dimensional subspace
........................365
21.2
The film, the wire and the grain
...................371
Contents xix
Part V
—
Applications
to Open
Systems
375
22.
Thermo
Algebras in Phase Space: Quantum and Classical
Systems
377
22.1
Wigner function for the
Schrödinger
field
.............. 377
22.2
Wigner function for the Klein-Gordon field
............. 381
22.3
Wigner function for the Dirac field
................. 383
22.4
Representations for classical systems
................ 385
22.4.1
Thermo-Lie groups for classical systems
..........385
22.4.2 517(1,1)
and the thermal classical oscillator
....... 387
22.5
Classical unitary representations
................... 389
22.6
Liouville equation for the oscillator
................. 394
22.7
Non-relativistic symmetries in the
Schönberg-Fock
space
..... 396
22.8
Classical relativistic representation
................. 398
22.9
Boltzmann equation and non-relativistic limit
........... 401
23.
Real-Time
Method for Nonequilibrium Quantum Mechanics
403
23.1 Schrödinger, Heisenberg
and Liouville pictures
...........404
23.2
Linear model for phase transition
..................406
23.3
Nonlinear model for phase transition
................408
23.3.1
Correlation functions in coherent state
...........409
23.3.2
Correlation functions in thermal state
...........411
23.4
Beyond the
Hartree
approximation for nonlinear model
......412
23.4.1
Beyond the
Hartree
approximation
.............413
23.4.2
Stability of the Liouville-
von
Neumann method
......415
23.5
TFD for time-dependent boson system
...............416
24.
Dressed and Bare State Approaches to the Thermalization Process
421
24.1
The model
............................... 422
24.2
The thermalization process in bare coordinates
.......... 425
24.3
Dressed coordinates and dressed states
............... 431
24.4
Thermal behavior for a cavity of arbitrary size with dressed
coordinates
............................... 433
24.5
The limit of arbitrarily large cavity: unbounded space
...... 435
Epilogue
441
Bibliography
445
Index
457
|
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| id | DE-604.BV035733654 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:53:15Z |
| institution | BVB |
| isbn | 9812818871 9789812818874 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018010203 |
| oclc_num | 633996099 |
| open_access_boolean | |
| owner | DE-29T DE-355 DE-BY-UBR DE-11 DE-91G DE-BY-TUM |
| owner_facet | DE-29T DE-355 DE-BY-UBR DE-11 DE-91G DE-BY-TUM |
| physical | XIX, 461 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Thermal quantum field theory algebraic aspects and applications Faqir C. Khanna ... Singapore [u.a.] World Scientific 2009 XIX, 461 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Endliche Temperatur (DE-588)4736704-0 gnd rswk-swf Symmetrie (DE-588)4058724-1 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 s Endliche Temperatur (DE-588)4736704-0 s Symmetrie (DE-588)4058724-1 s DE-604 Khanna, Faqir C. Sonstige oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018010203&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Thermal quantum field theory algebraic aspects and applications Endliche Temperatur (DE-588)4736704-0 gnd Symmetrie (DE-588)4058724-1 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4736704-0 (DE-588)4058724-1 (DE-588)4047984-5 |
| title | Thermal quantum field theory algebraic aspects and applications |
| title_auth | Thermal quantum field theory algebraic aspects and applications |
| title_exact_search | Thermal quantum field theory algebraic aspects and applications |
| title_full | Thermal quantum field theory algebraic aspects and applications Faqir C. Khanna ... |
| title_fullStr | Thermal quantum field theory algebraic aspects and applications Faqir C. Khanna ... |
| title_full_unstemmed | Thermal quantum field theory algebraic aspects and applications Faqir C. Khanna ... |
| title_short | Thermal quantum field theory |
| title_sort | thermal quantum field theory algebraic aspects and applications |
| title_sub | algebraic aspects and applications |
| topic | Endliche Temperatur (DE-588)4736704-0 gnd Symmetrie (DE-588)4058724-1 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Endliche Temperatur Symmetrie Quantenfeldtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018010203&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT khannafaqirc thermalquantumfieldtheoryalgebraicaspectsandapplications |