Mathematics of quantization and quantum fields:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2013
|
| Edition: | 1. publ. |
| Series: | Cambridge monographs on mathematical physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 674 S. graph. Darst. |
| ISBN: | 9781107011113 |
Staff View
MARC
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| 245 | 1 | 0 | |a Mathematics of quantization and quantum fields |c Jan Dereziński ; Christian Gérard |
| 250 | |a 1. publ. | ||
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| 300 | |a XII, 674 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804150203012349955 |
|---|---|
| adam_text | Contents
Dedication
po-ge
vii
Introduction
1
1
Vector spaces
8
1.1
Elementary linear algebra
8
1.2
Complex vector spaces
17
1.3
Complex structures
23
1.4
Groups and Lie algebras
32
1.5
Notes
35
2
Operators in Hilbert spaces
36
2.1
Convergence and completeness
36
2.2
Bounded and unbounded operators
38
2.3
Functional calculus
45
2.4
Polar decomposition
53
2.5
Notes
56
3
Tensor algebras
57
3.1
Direct sums and tensor products
57
3.2
Tensor algebra
64
3.3
Symmetric and anti-symmetric tensors
65
3.4
Creation and annihilation operators
73
3.5
Multi-linear symmetric and anti-symmetric forms
78
3.6
Volume forms, determinant and Pfaffian
85
3.7
Notes
91
4
Analysis in L2(Rd)
92
4.1
Distributions and the Fourier transformation
92
4.2
Weyl operators
100
4.3
x, D-quantization
106
4.4
Notes
110
5
Measures 111
5.1
General measure theory 111
5.2
Finite measures on real Hilbert spaces
121
χ
Contents
5.3
Weak distributions and the Minlos-Sazonov theorem
126
5.4
Gaussian measures on real Hubert spaces
132
5.5
Gaussian measures on complex Hubert spaces
136
5.6
Notes
141
6
Algebras
142
6.1
Algebras
142
6.2
C*- and W-algebras
144
6.3
Tensor products of algebras
151
6.4
Modular theory
151
6.5
Non-commutative probability spaces
155
6.6
Notes
158
7
Anti-symmetric calculus
159
7.1
Basic anti-symmetric calculus
159
7.2
Operators and anti-symmetric calculus
167
7.3
Notes
172
8
Canonical commutation relations
173
8.1
CCR representations
173
8.2
Field operators
180
8.3
CCR algebras
188
8.4
Weyl-Wigner quantization
196
8.5
General coherent vectors
203
8.6
Notes
210
9
CCR on Fock space
212
9.1
Fock CCR representation
213
9.2
CCR on anti-holomorphic Gaussian L2 spaces
216
9.3
CCR on real Gaussian L2 spaces
218
9.4
Wick and
anti-
Wick bosonic quantization
226
9.5
Notes
238
10
Symplectic
invariance
of CCR in
finite-dimensions
239
10.1
Classical quadratic Hamiltonians
239
10.2
Quantum quadratic Hamiltonians
245
10.3
Metaplectic group
250
10.4
Symplectic group on a space with conjugation
258
10.5
Metaplectic group in the
Schrödinger
representation
262
10.6
Notes
265
11
Symplectic
invariance
of the CCR
on Fock spaces
266
11.1
Symplectic group on
a
Kahler
space
266
11.2
Bosonic quadratic Hamiltonians on Fock spaces
276
Contents xi
11.3 Bosonic Bogoliubov
transformations
on Fock spaces
283
11.4 Fock
sector of a CCR representation
287
11.5
Coherent sector of CCR representations
301
11.6
van Hove Hamiltonians
304
11.7
Notes
312
12
Canonical anti-commutation relations
313
12.1
CAR representations
313
12.2
CAR representations in finite dimensions
319
12.3
CAR algebras: finite dimensions
323
12.4
Anti-symmetric quantization and real-wave CAR representation
326
12.5
CAR algebras: infinite dimensions
331
12.6
Notes
336
13
CAR on Fock spaces
337
13.1
Fock CAR representation
337
13.2
Real-wave and complex-wave CAR representation on Fock spaces
339
13.3
Wick and
anti-
Wick fermionic quantization
345
13.4
Notes
350
14
Orthogonal
invariance
of CAR algebras
351
14.1
Orthogonal groups
351
14.2
Quadratic fermionic Hamiltonians
354
14.3
Pirf and Pin groups
358
14.4
Notes
367
15
Clifford relations
368
15.1
Clifford algebras
368
15.2
Quaternions
370
15.3
Clifford relations over
Μ« ρ
373
15.4
Clifford algebras over W*
382
15.5
Notes
385
16
Orthogonal
invariance
of the CAR on Fock spaces
386
16.1
Orthogonal group on
a
Kahler
space
386
16.2
Fermionic quadratic Hamiltonians on Fock spaces
399
16.3
Fermionic Bogoliubov transformations on Fock spaces
404
16.4
Fock sector of a CAR representation
417
16.5
Notes
421
17
Quasi-free states
423
17.1
Bosonic quasi-free states
424
17.2
Fermionic quasi-free states
444
17.3
Lattices of
von
Neumann algebras on a Fock space
462
17.4
Notes
473
xii Contents
18
Dynamics of quantum fields
475
18.1
Neutral systems
478
18.2
Charged systems
484
18.3
Abstract Klein-Gordon equation and its quantization
492
18.4
Abstract Dirac equation and its quantization
504
18.5
Notes
511
19
Quantum fields on space-time
512
19.1
Minkowski space and the
Poincaré
group
513
19.2
Quantization of the Klein-Gordon equation
516
19.3
Quantization of the Dirac equation
525
19.4
Partial differential equations on manifolds
537
19.5
Generalized Klein-Gordon equation on curved space-time
542
19.6
Generalized Dirac equation on curved space-time
549
19.7
Notes
554
20
Diagrammatics
555
20.1
Diagrams and Gaussian integration
557
20.2
Perturbations of quantum dynamics
570
20.3 Friedrichs
diagrams and products of Wick monomials
575
20.4 Friedrichs
diagrams and the scattering operator
582
20.5
Feynman diagrams and vacuum expectation value
588
20.6
Feynman diagrams and the scattering operator
600
20.7
Notes
604
21
Euclidean approach for bosons
605
21.1
A simple example: Brownian motion
607
21.2
Euclidean approach at zero temperature
609
21.3
Perturbations of Markov path spaces
619
21.4
Euclidean approach at positive temperatures
624
21.5
Perturbations of /3-Markov path spaces
636
21.6
Notes
639
22
Interacting bosonic fields
641
22.1
Free bosonic fields
641
22.2
Ρ (ψ)
interaction
646
22.3
Scattering theory for space-cutoff
Ρ (φ)
2
Hamiltonians
656
22.4
Notes
660
References
661
Symbols index
668
Subject index
671
|
| any_adam_object | 1 |
| author | Dereziński, Jan 1957- Gérard, Christian 1960- |
| author_GND | (DE-588)11520816X (DE-588)134231864 |
| author_facet | Dereziński, Jan 1957- Gérard, Christian 1960- |
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| author_sort | Dereziński, Jan 1957- |
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| building | Verbundindex |
| bvnumber | BV040911128 |
| classification_rvk | SK 950 UK 1000 UK 1200 |
| classification_tum | PHY 011f PHY 023f |
| ctrlnum | (OCoLC)840417641 (DE-599)HBZHT017479925 |
| dewey-full | 530.1430151 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1430151 |
| dewey-search | 530.1430151 |
| dewey-sort | 3530.1430151 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV040911128 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:35:06Z |
| institution | BVB |
| isbn | 9781107011113 |
| language | English |
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| spelling | Dereziński, Jan 1957- Verfasser (DE-588)11520816X aut Mathematics of quantization and quantum fields Jan Dereziński ; Christian Gérard 1. publ. Cambridge Cambridge University Press 2013 XII, 674 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge monographs on mathematical physics Quantentheorie (DE-588)4047992-4 gnd rswk-swf Feldquantisierung (DE-588)4153946-1 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Geometrische Quantisierung (DE-588)4156720-1 gnd rswk-swf Geometrische Quantisierung (DE-588)4156720-1 s Quantentheorie (DE-588)4047992-4 s DE-604 Feldquantisierung (DE-588)4153946-1 s Mathematische Physik (DE-588)4037952-8 s Gérard, Christian 1960- Verfasser (DE-588)134231864 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025890453&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dereziński, Jan 1957- Gérard, Christian 1960- Mathematics of quantization and quantum fields Quantentheorie (DE-588)4047992-4 gnd Feldquantisierung (DE-588)4153946-1 gnd Mathematische Physik (DE-588)4037952-8 gnd Geometrische Quantisierung (DE-588)4156720-1 gnd |
| subject_GND | (DE-588)4047992-4 (DE-588)4153946-1 (DE-588)4037952-8 (DE-588)4156720-1 |
| title | Mathematics of quantization and quantum fields |
| title_auth | Mathematics of quantization and quantum fields |
| title_exact_search | Mathematics of quantization and quantum fields |
| title_full | Mathematics of quantization and quantum fields Jan Dereziński ; Christian Gérard |
| title_fullStr | Mathematics of quantization and quantum fields Jan Dereziński ; Christian Gérard |
| title_full_unstemmed | Mathematics of quantization and quantum fields Jan Dereziński ; Christian Gérard |
| title_short | Mathematics of quantization and quantum fields |
| title_sort | mathematics of quantization and quantum fields |
| topic | Quantentheorie (DE-588)4047992-4 gnd Feldquantisierung (DE-588)4153946-1 gnd Mathematische Physik (DE-588)4037952-8 gnd Geometrische Quantisierung (DE-588)4156720-1 gnd |
| topic_facet | Quantentheorie Feldquantisierung Mathematische Physik Geometrische Quantisierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025890453&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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