Generalized coherent states and their applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1986
|
| Series: | Texts and monographs in physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XI, 320 S. |
| ISBN: | 9783540159124 0387159126 |
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MARC
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| 245 | 1 | 0 | |a Generalized coherent states and their applications |c A. Perelomov |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1986 | |
| 300 | |a XI, 320 S. | ||
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| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Coherent states | |
| 650 | 4 | |a Lie groups | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Symmetric spaces | |
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Record in the Search Index
| _version_ | 1804116730336772096 |
|---|---|
| adam_text | Contents
Introduction
................................................... 1
Parti
Generalized Coherent States for the Simplest Lie Groups
1.
Standard System of Coherent States Related to the
Heisenberg-
Weyl
Group: One Degree of Freedom
............................... 7
1.1
The
Heisenberg-
Weyl Group and Its Representations
........ 8
1.1.1
The Heisenberg-Weyl Group
......................... 8
1.1.2
Representations of the Heisenberg-Weyl Group
........ 11
1.1.3
Concrete Realization of the Representation Tx(g)
...... 12
1.2
Coherent States
......................................... 13
1.3
The Fock-Bargmann Representation
....................... 19
1.4
Completeness of Coherent-State Subsystems
................ 23
1.5
Coherent States and Theta Functions
...................... 26
1.6
Operators and Their Symbols
............................. 29
1.7
Characteristic Functions
.................................. 37
2.
Coherent States for Arbitrary Lie Groups
....................... 40
2.1
Definition of the Generalized Coherent State
................ 40
2.2
General Properties of Coherent-State Systems
............... 42
2.3
Completeness and Expansion in States of the CS System
....... 43
2.4
Selection of Generalized CS Systems with States Closest to
Classical
............................................... 44
3.
The Standard System of Coherent States; Several Degrees of Freedom
48
3.1
General Properties
....................................... 48
3.2
Coherent States and Theta Functions for Several Degrees of
Freedom
............................................... 50
4.
Coherent States for the Rotation Group of Three-Dimensional Space
54
4.1
Structure of the Groups SO(3) and SU(2)
.................. 54
4.2
Representations of SUQ)
................................. 58
4.3
Coherent States
......................................... 59
VIII Contents
5.
The Most Elementary Noncompact, Non-Abelian Simple Lie Group:
st
/α,ΐ)
...................................................
67
5.1
Group SU(i,
1)
and Its Representations
.................... 67
5.1.1
Fundamental Properties of SU(i,
1)................... 67
5.1.2
Discrete Series
..................................... 70
5.1.3
Principal (Continuous) Series
........................ 71
5.2
Coherent States
......................................... 73
5.2.1
Discrete Series
..................................... 73
5.2.2
Principal (Continuous) Series
........................ 76
6.
The
Lorentz
Group: SO(3,
1) ................................. 84
6.1
Representations of the
Lorentz
Group
..................... 84
6.2
Coherent States
......................................... 86
7.
Coherent States for the SO(n,
1)
Group: Class-I Representations of the
Principal Series
............................................. 93
7.1
Class-I Representations of SO(n,
1)........................ 93
7.2
Coherent States
......................................... 94
8.
Coherent States for a Bosonic System with Finite Number of Degrees of
Freedom
................................................... 101
8.1
Canonical Transformations
............................... 101
8.2
Coherent States
......................................... 104
8.3
Operators in the Space
Жв{+)
.............................. 107
9.
Coherent States for a Fermionic System with Finite Number of Degrees
of Freedom
.................................................
Ill
9.1
Canonical Transformations
...............................
Ill
9.2
Coherent States
......................................... 113
9.3
Operators in the Space
JťP{+)
.............................. 114
Part II
General Case
10.
Coherent States for
Nilpotent
Lie Groups
...................... 119
10.1
Structure of
Nilpotent
Lie Groups
...................... 119
10.2
Orbits of Coadjoint Representation
...................... 120
10.3
Orbits of
Nilpotent
Lie Groups
......................... 121
10.4
Representations of
Nilpotent
Lie Groups
................. 122
10.5
Coherent States
....................................... 124
11.
Coherent States for Compact
Semisimple
Lie Groups
............ 126
11.1
Elements of the Theory of Compact
Semisimple
Lie Groups
. 126
11.2
Representations of Compact Simple Lie Groups
........... 128
11.3
Coherent States
....................................... 130
Contents
IX
12.
Discrete
Series
of Representations: The General Case
............ 134
12.1
Discrete Series
........................................ 134
12.2
Bounded Domains
..................................... 135
12.3
Coherent States
....................................... 139
13.
Coherent States for Real
Semisimple
Lie Groups:
Class-I Representations of Principal Series
..................... 145
13.1
Class-I Representations
................................ 145
13.2
Coherent States
....................................... 147
13.3
Horocycles
in Symmetric Space
......................... 148
13.4
Rank-1 Symmetric Spaces
.............................. 149
13.5
Properties of Rank-1 CS Systems
........................ 152
13.6
Complex Homogeneous Bounded Domains
............... 161
13.6.1
Туре
-I
Tube Domains
........................... 164
13.6.2
Type-II Tube Domains
.......................... 166
13.6.3
Type-Ill Tube Domains
.......................... 167
13.6.4
Туре
-IV
Domains
............................... 168
13.6.5
The Exceptional Domain Dv
..................... 170
13.7
Properties of the Coherent States
........................ 170
14.
Coherent States and Discrete Subgroups:
The Case of SU{1,1)
....................................... 173
14.1
Preliminaries
......................................... 173
14.2
Incompleteness Criterion for CS Subsystems Related to
Discrete Subgroups
.................................... 174
14.3
Growth of a Function Analytical in a Disk Related to the
Distribution of Its Zeros
............................... 176
14.4
Completeness Criterion for CS Subsystems
................ 178
14.5
Discrete Subgroups of SU(1,
1)
and Automorphic Forms
... 179
15.
Coherent States for Discrete Series and Discrete Subgroups:
General Case
.............................................. 182
15.1
Automorphic Forms
................................... 182
15.2
Completeness of Some CS Subsystems
................... 183
16.
Coherent States and Berezin s Quantization
.................... 185
16.1
Classical Mechanics
.................................... 186
16.2
Quantization
.......................................... 189
16.3
Quantization on the Lobachevsky Plane
.................. 191
16.3.1
Description of Operators
......................... 192
16.3.2
The Correspondence Principle
.................... 193
16.3.3
Operator Th
m
Terms of a Laplacian
.............. 194
16.3.4
Representation of Group of Motions of the
Lobachevsky Plane in Space J<i
................... 195
X
Contents
16.3.5
Quantization by Inversions Analog to
Weyl Quantization
.............................. 196
16.4
Quantization on a Sphere
.............................. 197
16.5
Quantization on Homogeneous
Kahler
Manifolds
.......... 199
Part III
Physical Applications
17.
Preliminaries
.............................................. 207
18.
Quantum Oscillators
....................................... 211
18.1
Quantum Oscillator Acted on by a Variable External Force
. 211
18.2
Parametric Excitation of a Quantum Oscillator
............ 213
18.3
Quantum Singular Oscillator
............................ 217
18.3.1
The Stationary Case
............................. 217
18.3.2
The Nonstationary Case
......................... 220
18.3.3
The Case of
N
Interacting Particles
................ 222
18.4
Oscillator with Variable Frequency Acted on by an
External Force
........................................ 227
19.
Particles in External Electromagnetic Fields
.................... 231
19.1
Spin Motion in a Variable Magnetic Field
................ 231
19.2
Boson Pair Production in a Variable Homogeneous
External Field
........................................ 233
19.2.1
Dynamical Symmetry for Scalar Particles
........... 233
19.2.2
The Multidimensional Case: Coherent States
....... 237
19.2.3
The Multidimensional Case
:
Nonstationary Problem
. 241
19.3
Fermion Pair Production in a Variable Homogeneous
External Field
........................................ 242
19.3.1
Dynamical Symmetry for Spin-1/2 particles
......... 242
19.3.2 Heisenberg
Representation
....................... 245
19.3.3
The Multidimensional Case: Coherent States
....... 248
20.
Generating Function for Clebsch-Gordan Coefficients of
the SU{2) group
........................................... 253
21.
Coherent States and the Quasiclassical limit
................... 256
22.
Í/N
Expansion for Gross-Neveu Models
....................... 260
22.1
Description of the Model
............................... 260
22.2
Dimensionality of Space
Жц=Щ,
in the Fermion Case
...... 265
22.3
Quasiclassical Limit
.................................... 266
Contents
XI
23. Relaxation
to Thermodynamic Equilibrium .....................
270
23.1 Relaxation
of
Quantum
Oscillator to
Thermodynamic
Equilibrium
............................ 270
23.1.1
Kinetic Equation
............................... 270
23.1.2
Characteristic Functions and Quasiprobability
Distributions
................................... 271
23.1.3
Use of Operator Symbols
........................ 274
23.2
Relaxation of a Spinning Particle to Thermodynamic
Equilibrium in the Presence of a Magnetic Field
........... 278
24.
Landau Diamagnetism
...................................... 282
25.
The Heisenberg-Euler Lagrangian
............................. 286
26.
Synchrotron Radiation
...................................... 289
27.
Classical and
Quantal
Entropy
............................... 292
Appendix A. Proof of Completeness for Certain CS Subsystems
...... 296
Appendix B. Matrix Elements of the Operator
D
(γ) ................
300
Appendix
С.
Jacobians of Group Transformations for Classical Domains
305
Further Applications of the CS Method
.......................... 308
References
.................................................... 311
Subject-Index
................................................. 319
Addendum. Further Applications of the CS Method
................ 308
References
.................................................... 311
References to Addendum
.................................... 316
Subject-Index
................................................. 319
|
| any_adam_object | 1 |
| author | Perelomov, Askolʹd M. 1935- |
| author_GND | (DE-588)11069547X |
| author_facet | Perelomov, Askolʹd M. 1935- |
| author_role | aut |
| author_sort | Perelomov, Askolʹd M. 1935- |
| author_variant | a m p am amp |
| building | Verbundindex |
| bvnumber | BV002272492 |
| callnumber-first | Q - Science |
| callnumber-label | QC20 |
| callnumber-raw | QC20.7.L54 |
| callnumber-search | QC20.7.L54 |
| callnumber-sort | QC 220.7 L54 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 340 SK 950 |
| classification_tum | PHY 012f |
| ctrlnum | (OCoLC)12972287 (DE-599)BVBBV002272492 |
| dewey-full | 530.1/5255 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1/5255 |
| dewey-search | 530.1/5255 |
| dewey-sort | 3530.1 45255 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV002272492 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:43:09Z |
| institution | BVB |
| isbn | 9783540159124 0387159126 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001493096 |
| oclc_num | 12972287 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-703 DE-355 DE-BY-UBR DE-20 DE-29T DE-19 DE-BY-UBM DE-634 DE-706 DE-83 DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-703 DE-355 DE-BY-UBR DE-20 DE-29T DE-19 DE-BY-UBM DE-634 DE-706 DE-83 DE-11 DE-188 |
| physical | XI, 320 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Springer |
| record_format | marc |
| series2 | Texts and monographs in physics |
| spelling | Perelomov, Askolʹd M. 1935- Verfasser (DE-588)11069547X aut Generalized coherent states and their applications A. Perelomov Berlin [u.a.] Springer 1986 XI, 320 S. txt rdacontent n rdamedia nc rdacarrier Texts and monographs in physics Hier auch später erschienene, unveränderte Nachdrucke Coherentie (natuurkunde) gtt Espaces symétriques Lie, Groupes de Physique mathématique Toepassingen gtt Mathematische Physik Coherent states Lie groups Mathematical physics Symmetric spaces Symmetrische Gruppe (DE-588)4184204-2 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Kohärenter Zustand (DE-588)4125526-4 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Kohärenter Zustand (DE-588)4125526-4 s Lie-Gruppe (DE-588)4035695-4 s DE-604 Mathematische Physik (DE-588)4037952-8 s Physik (DE-588)4045956-1 s Mathematische Methode (DE-588)4155620-3 s Symmetrische Gruppe (DE-588)4184204-2 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001493096&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Perelomov, Askolʹd M. 1935- Generalized coherent states and their applications Coherentie (natuurkunde) gtt Espaces symétriques Lie, Groupes de Physique mathématique Toepassingen gtt Mathematische Physik Coherent states Lie groups Mathematical physics Symmetric spaces Symmetrische Gruppe (DE-588)4184204-2 gnd Mathematische Methode (DE-588)4155620-3 gnd Mathematische Physik (DE-588)4037952-8 gnd Lie-Gruppe (DE-588)4035695-4 gnd Kohärenter Zustand (DE-588)4125526-4 gnd Physik (DE-588)4045956-1 gnd |
| subject_GND | (DE-588)4184204-2 (DE-588)4155620-3 (DE-588)4037952-8 (DE-588)4035695-4 (DE-588)4125526-4 (DE-588)4045956-1 |
| title | Generalized coherent states and their applications |
| title_auth | Generalized coherent states and their applications |
| title_exact_search | Generalized coherent states and their applications |
| title_full | Generalized coherent states and their applications A. Perelomov |
| title_fullStr | Generalized coherent states and their applications A. Perelomov |
| title_full_unstemmed | Generalized coherent states and their applications A. Perelomov |
| title_short | Generalized coherent states and their applications |
| title_sort | generalized coherent states and their applications |
| topic | Coherentie (natuurkunde) gtt Espaces symétriques Lie, Groupes de Physique mathématique Toepassingen gtt Mathematische Physik Coherent states Lie groups Mathematical physics Symmetric spaces Symmetrische Gruppe (DE-588)4184204-2 gnd Mathematische Methode (DE-588)4155620-3 gnd Mathematische Physik (DE-588)4037952-8 gnd Lie-Gruppe (DE-588)4035695-4 gnd Kohärenter Zustand (DE-588)4125526-4 gnd Physik (DE-588)4045956-1 gnd |
| topic_facet | Coherentie (natuurkunde) Espaces symétriques Lie, Groupes de Physique mathématique Toepassingen Mathematische Physik Coherent states Lie groups Mathematical physics Symmetric spaces Symmetrische Gruppe Mathematische Methode Lie-Gruppe Kohärenter Zustand Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001493096&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT perelomovaskolʹdm generalizedcoherentstatesandtheirapplications |