Quantum field theory and its macroscopic manifestations: boson condensation, ordered patterns and topological defects
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| Format: | Book |
| Language: | English |
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London
Imperial College Press
2011
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 526 S. graph. Darst. |
| ISBN: | 9781848162808 1848162804 |
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MARC
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| 245 | 1 | 0 | |a Quantum field theory and its macroscopic manifestations |b boson condensation, ordered patterns and topological defects |c Massimo Blasone & Giuseppe Vitiello ; Petr Jizba |
| 264 | 1 | |a London |b Imperial College Press |c 2011 | |
| 300 | |a XVIII, 526 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 |
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| 700 | 1 | |a Vitiello, Giuseppe |e Verfasser |0 (DE-588)139068643 |4 aut | |
| 700 | 1 | |a Jizba, Petr |e Verfasser |0 (DE-588)1011805170 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-020674855 | ||
Record in the Search Index
| _version_ | 1804143423885672448 |
|---|---|
| adam_text | Contents
Preface
vii
1.
The .structure of the space of the physical states
1
1.1
Introduction
......................... 1
1.2
The space of the states of physical particles
........ 2
1.3
The
Weyl Heisenberg
algebra and the Fork
spaco
.... 7
1.4
Irreducible representations of the canonical commutation
relations
........................... 10
1.5
Unitarily equivalent representations
............ 15
1.6
The Stone-
von
Neumann theorem
............. 17
1.7
Unitarily inequivalent representations
........... 19
1.8
The deformation of Weyl-Heisenberg algebra
....... 21
1.8.1
Self-similarity, fractals and the Fock-
Bargmann
representation
.................... 26
1.9
The physical particle energy and momentum operator
. . 30
1.10
The physical Fock space and the physical fields
...... 32
Appendix A Strong limit and weak limit
35
Appendix
В
Glauber coherent states
47
Appendix
С
Generalized coherent states
41
Appendix
D q-
WH
algebra, coherent states and theta func¬
tions
49
xiv
Quantum Field Theory and its Macroscopic Manifestations
2.
Inequivalent representations of the canonical commuta¬
tion relations
53
2.1
Introduction
......................... 53
2.2 Heisenberg
fields, physical fields and the dynamical map
54
2.3
Examples of inequivalent representations
......... 58
2.4
The
Haag
theorem and non-perturbative physics
..... 66
2.5
The momentum operator
.................. 67
2.6
Time evolution and asymptotic limits
........... 68
2.7
Inequivalent representations in flavor mixing
....... 71
Appendix
E
Computation of
{0 фі{х) а,па.т)
85
Appendix
F
Computation of
0(θ))
87
Appendix
G
Orthogonality of flavor vacua at different times
89
Appendix
H
Entanglement in neutrino oscillations
91
3.
Spontaneous breakdown of symmetry and the
Goldstone
theorem
97
3.1
Introduction
......................... 97
3.2
Invariance
and symmetry
.................. 99
3.3
Irreducible representations of the symmetry group
.... 101
3.4
Symmetry and the vacuum manifold
............ 102
3.5
Boson transformation and inequivalent representations
. 106
3.6
Spontaneous symmetry breaking and functional integrals
. 108
3.7
The
Goldstone
theorem
................... 112
3.7.1 [7(1)
symmetry
................... 112
3.7.2
SU{2) symmetry
................... 115
3.8
Spontaneous symmetry breaking in local gauge theories
. 119
3.8.1
The
[7(1)
local gauge model
............ 119
3.8.2
The chiral gauge model
.............. 124
3.9
Finite volume effects
.................... 126
3.10
Space-time dimensionality
................. 128
Appendix I The order parameter space
133
Appendix
J
The Mermin-Wagner-Coleman theorem
135
Contents xv
4.
Dynamical rearrangement of symmetry and macroscopic
manifestations of QFT
137
4.1
Introduction
......................... 137
4.2
Dynamical rearrangement of symmetry
.......... 139
4.2.1
SU
(2)
symmetry
.................. 139
4.2.2
Global U(l) symmetry
............... 143
4.2.3
Local U{1) symmetry and the emergence of classi¬
cal Maxwell equations
................ 145
4.3
The boson transformation theorem and the non-
homogeneous boson condensation
............. 153
4.3.1
Topological singularities, gapless modes and
macroscopic
observables
.............. 156
4.3.2
Defect formation in the process of symmetry
breaking phase transitions
............. 158
4.4
Group contraction and spontaneous symmetry breaking
. 159
4.4.1
The infrared effect
.................. 159
4.4.2
Group contraction, boson condensation and
macroscopic quantum systems
........... 165
4.4.3
The collective behavior of quantum components
and group contraction
............... 166
4.5
Quantum fluctuations and macroscopic stability
...... 169
4.5.1
Quantum mechanical decoherence and stability of
macroscopic quantum systems
........... 174
Appendix
К
Group contraction and Virasoro algebra
179
Appendix
L
Phase locking in the
N
atom system
183
5.
Thermal field theory and trajectories in the space of the
representations
185
5.1
Introduction
......................... 185
5.2
Doubling the degrees of freedom
.............. 188
5.2.1
The two-slit experiment
............... 189
5.3
Thermo Field Dynamics: A brief introduction
....... 191
5.3.1
The propagator structure in TFD
......... 199
5.3.2
Non-hermitian representation of TFD
...... 201
5.3.3
TFD for fields with continuous mass spectrum
. . 202
xvi
Quantum Field Theory and its Macroscopic Manifestations
5.4
The g-deformed
Hopf
algebra and the doubling of the field
degrees of freedom
...................... 206
5.5
Free energy, entropy and the arrow of time. Intrinsic ther¬
mal nature of QFT
..................... 212
5.5.1
Entropy and system-environment entanglement
. 214
5.6
Thermal field theory and the gauge field
......... 215
5.7
Boson condensation at finite temperature
......... 221
5.7.1
Free energy and classical energy
.......... 225
5.8
Trajectories in the space of representations
........ 231
6.
Selected topics in thermal field theory
235
6.1
Introduction
......................... 235
6.2
The Gell-Mann-Low formula and the closed time-path for¬
malism
............................ 236
6.3
The functional integral approach
.............. 240
6.3.1
Generating functionals for Green s functions
. . . 240
6.3.2
The Feynman-Matthews-Salam formula
..... 246
6.3.3
More on generating functionals
........... 249
6.4
The effective action and the Schwinger-Dyson equations
. 252
6.5
Imaginary-time formalism
.................. 257
6.6
Geometric background for thermal field theories
...... 260
6.6.1
The
η-ξ
spacetime
.................. 261
6.6.2
Fields in
η-ξ
spacetime
............... 264
Appendix
M
Thermal Wick theorem
271
Appendix
N
Coherent state functional integrals
275
N.I Glauber coherent states
................... 275
N.2 Generalized coherent states
................. 279
Appendix
О
Imaginary-time formalism and phase transitions
287
O.I Landau-Ginzburg treatment
................. 290
Appendix
Ρ
Proof of Bogoliubov inequality
293
7.
Topological defects as non-homogeneous condensates. I
297
7.1
Introduction
.......................... 297
7.2
Quantum field dynamics and classical soliton solutions
. 298
Contents xvii
7.2.1
The dynamical map and the boson transformation
299
7.2.2
The quantum coordinate
.............. 302
7.3
The
λφ4
kink solution
.................... 304
7.3.1
The kink solution and temperature effects
.... 309
7.3.2
The kink solution: closed time-path approach
. . 312
7.4
The sine-Gordon solution
.................. 319
7.4.1
The quantum image of the
Bäcklund
transforma¬
tions
......................... 324
7.5
Soliton solutions of the non-linear
Schrödinger
equation
. 327
7.5.1
The ferromagnetic chain
.............. 328
7.5.2
Non-linear
Schrödinger
equation with
Toda
lattice
back-reaction potential
............... 334
7.5.3
Ring solitons in the
Scheibe
aggregates
...... 336
7.6
Fermions
in topologically non-trivial background fields
. 339
7.7
Superfluid vortices
...................... 344
8.
Topological defects as non-hornogeneous condensates. II
349
8.1
Introduction
......................... 349
8.2
Vortices in U(l) local gauge theory
............ 350
8.3
Topological solitons in gauge theories
........... 353
8.3.1
Homogeneous boson condensation
......... 357
8.3.2
The vortex of scalar electrodynamics
....... 359
8.3.3
The t Hooft-Polyakov
monopole
......... 362
8.3.4
Thesphaleron
.................... 365
8.4
The SU(2)
instanton
.................... 367
9.
Dissipation and quantization
373
9.1
Introduction
......................... 373
9.2
The exact action for damped motion
........... 374
9.2.1
Quantum Brownian motion
............ 378
9.3
Quantum dissipation and unitarily inequivalent represen¬
tations in QFT
........................ 379
9.3.1
The arrow of time and squeezed coherent states
. 383
9.4
Dissipative non-commutative plane
............. 385
9.4.1
The dissipative quantum phase interference
. . . 388
9.5
Gauge structure and thermal features in particle mixing
. 390
9.6
Dissipation and the many-body model of the brain
.... 396
9.7
Quantization and dissipation
................ 404
xviii
Quantum Field Theory and its Macroscopic Manifestations
Appendix
Q
Entropy and geometrical phases in neutrino mixing
413
Appendix
R
Trajectories in the memory space
417
10.
Elements of soliton theory and related concepts
423
10.1
Introduction
.......................... 423
10.2
The Korteweg-de
Vries
soliton
............... 424
10.3
Topological solitons in
(1 +
l)-d relativistic field theories
. 428
10.3.1
The sine-Gordon soliton
.............. 429
10.3.2
The
ХфА
kink
.................... 431
10.4
Topological solitons in gauge theories
............ 434
10.4.1
The Nielsen-Olesen vortex
............. 434
10.4.2
The
t Hooft-Polyakov monopole
......... 438
10.5
Topological defect classification and the Kibble-Zurek
mechanism for defect formation
.............. 442
10.5.1
Exact homotopy sequences
.............. 445
10.5.2
Topological defects in theories with SSB
..... 447
10.6
Derrick theorem and defect stability
............ 453
10.7
Bogomol nyi bounds
..................... 458
10.8
Non-topological solitons
................... 463
10.9
Instantons
and their manifestations
............. 466
10.9.1
Collective coordinates and fermionic zero modes
. 480
Appendix
S
Bäcklund
transformation for the sine-Gordon
system
483
Appendix
T
Elements of homotopy theory
487
Bibliography
497
Index
519
|
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| author_GND | (DE-588)1011804719 (DE-588)139068643 (DE-588)1011805170 |
| author_facet | Blasone, Massimo 1967- Vitiello, Giuseppe Jizba, Petr |
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| id | DE-604.BV036757721 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:47:26Z |
| institution | BVB |
| isbn | 9781848162808 1848162804 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020674855 |
| oclc_num | 699590291 |
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| owner_facet | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 |
| physical | XVIII, 526 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Imperial College Press |
| record_format | marc |
| spelling | Blasone, Massimo 1967- Verfasser (DE-588)1011804719 aut Quantum field theory and its macroscopic manifestations boson condensation, ordered patterns and topological defects Massimo Blasone & Giuseppe Vitiello ; Petr Jizba London Imperial College Press 2011 XVIII, 526 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 s DE-604 Vitiello, Giuseppe Verfasser (DE-588)139068643 aut Jizba, Petr Verfasser (DE-588)1011805170 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020674855&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blasone, Massimo 1967- Vitiello, Giuseppe Jizba, Petr Quantum field theory and its macroscopic manifestations boson condensation, ordered patterns and topological defects Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4047984-5 |
| title | Quantum field theory and its macroscopic manifestations boson condensation, ordered patterns and topological defects |
| title_auth | Quantum field theory and its macroscopic manifestations boson condensation, ordered patterns and topological defects |
| title_exact_search | Quantum field theory and its macroscopic manifestations boson condensation, ordered patterns and topological defects |
| title_full | Quantum field theory and its macroscopic manifestations boson condensation, ordered patterns and topological defects Massimo Blasone & Giuseppe Vitiello ; Petr Jizba |
| title_fullStr | Quantum field theory and its macroscopic manifestations boson condensation, ordered patterns and topological defects Massimo Blasone & Giuseppe Vitiello ; Petr Jizba |
| title_full_unstemmed | Quantum field theory and its macroscopic manifestations boson condensation, ordered patterns and topological defects Massimo Blasone & Giuseppe Vitiello ; Petr Jizba |
| title_short | Quantum field theory and its macroscopic manifestations |
| title_sort | quantum field theory and its macroscopic manifestations boson condensation ordered patterns and topological defects |
| title_sub | boson condensation, ordered patterns and topological defects |
| 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=020674855&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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