Mathematical topics between classical and quantum mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York [u.a.]
Springer
1998
|
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 529 S. graph. Darst. |
| ISBN: | 038798318X |
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| 245 | 1 | 0 | |a Mathematical topics between classical and quantum mechanics |c N. P. Landsman |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1998 | |
| 300 | |a XIX, 529 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804127058652037120 |
|---|---|
| adam_text | N.P. LANDSMAN MATHEMATICAL TOPICS BETWEEN CLASSICAL AND QUANTUM
MECHANICS WITH 15 ILLUSTRATIONS SPRINGER CONTENTS PREFACE VUE SUBJECT
MATTER VII PREREQUISITES, LEVEL, AND ORGANIZATION OF THE BOOK VIII
CONVENTIONS AND NOTATION IX GENERAL IX FUNCTIONAL ANALYSIS IX HUBERT
SPACES X C*-ALGEBRAS X GROUP REPRESENTATIONS AND ACTIONS XI DIFFERENTIAL
GEOMETRY XI ACKNOWLEDGEMENTS XIII INTRODUCTORY OVERVIEW L I. OBSERVABLES
AND PURE STATES 1 OBSERVABLES 1 PURE STATES 3 FROM PURE STATES TO
OBSERVABLES 5 II. QUANTIZATION AND THE CLASSICAL LIMIT 7 FOUNDATIONS 8
QUANTIZATION ON FLAT SPACE 10 QUANTIZATION ON RIEMANNIAN MANIFOLDS 13
III. GROUPS, BUNDLES, AND GROUPOIDS 14 LIE GROUPS AND LIE ALGEBRAS 14
INTERNAL SYMMETRIES AND EXTERNAL GAUGE FIELDS 17 LIE GROUPOIDS AND LIE
ALGEBROIDS 21 IV. REDUCTION AND INDUCTION 25 REDUCTION 25 XVI CONTENTS
INDUCTION 28 APPLICATIONS IN RELATIVISTIC QUANTUM THEORY 32 I
OBSERVABLES AND PURE STATES 37 1 THE STRUCTURE OF ALGEBRAS OF
OBSERVABLES 37 1.1 JORDAN-LIE ALGEBRAS AND C*- ALGEBRAS 37 1.2 SPECTRUM
AND COMMUTATIVE C*- ALGEBRAS 41 1.3 POSITIVITY, ORDER, AND MORPHISMS 45
1.4 STATES 49 1.5 REPRESENTATIONS AND THE GNS-CONSTRUCTION 52 1.6
EXAMPLES OF C*-ALGEBRAS AND STATE SPACES 55 1.7 VON NEUMANN ALGEBRAS 58
2 THE STRUCTURE OF PURE STATE SPACES 60 2.1 PURE STATES AND COMPACT
CONVEX SETS 60 2.2 PURE STATES AND IRREDUCIBLE REPRESENTATIONS 63 2.3
POISSON MANIFOLDS 65 2.4 THE SYMPLECTIC DECOMPOSITION OF A POISSON
MANIFOLD. 69 2.5 (PROJECTIVE) HUBERT SPACES AS SYMPLECTIC MANIFOLDS . .
71 2.6 REPRESENTATIONS OF POISSON ALGEBRAS 76 2.7 TRANSITION PROBABILITY
SPACES 80 2.8 PURE STATE SPACES AS TRANSITION PROBABILITY SPACES ... 82
3 FROM PURE STATES TO OBSERVABLES 84 3.1 POISSON SPACES WITH A
TRANSITION PROBABILITY 84 3.2 IDENTIFICATION OF THE ALGEBRA OF
OBSERVABLES 86 3.3 SPECTRAL THEOREM AND JORDAN PRODUCT 88 3.4 UNITARITY
AND LEIBNIZ RULE 90 3.5 ORTHOMODULAR LATTICES 92 3.6 LATTICES ASSOCIATED
WITH STATES AND OBSERVABLES .... 94 3.7 THE TWO-SPHERE PROPERTY IN A
PURE STATE SPACE .... 98 3.8 THE POISSON STRUCTURE ON THE PURE STATE
SPACE 103 3.9 AXIOMS FOR THE PURE STATE SPACE OF A C*-ALGEBRA . . . 104
II QUANTIZATION AND THE CLASSICAL LIMIT 108 1 FOUNDATIONS 108 1.1 STRICT
QUANTIZATION OF OBSERVABLES 108 1.2 CONTINUOUS FIELDS OF C* -ALGEBRAS
110 1.3 COHERENT STATES AND BEREZIN QUANTIZATION 112 1.4 COMPLETE
POSITIVITY 116 1.5 COHERENT STATES AND REPRODUCING KERNELS 122 2
QUANTIZATION ON FLAT SPACE 126 2.1 THE HEISENBERG GROUP AND ITS
REPRESENTATIONS 126 2.2 THE METAPLECTIC REPRESENTATION 129 2.3 BEREZIN
QUANTIZATION ON FLAT SPACE 133 2.4 PROPERTIES OF BEREZIN QUANTIZATION ON
FLAT SPACE ... 137 2.5 WEYL QUANTIZATION ON FLAT SPACE 140 CONTENTS XVUE
2.6 STRICT QUANTIZATION AND CONTINUOUS FIELDS ON FLAT SPACE 144 2.7 THE
CLASSICAL LIMIT OF THE DYNAMICS 148 3 QUANTIZATION ON RIEMANNIAN
MANIFOLDS 154 3.1 SOME AFFINE GEOMETRY 154 3.2 SOME RIEMANNIAN GEOMETRY
157 3.3 HAMILTONIAN RIEMANNIAN GEOMETRY 159 3.4 WEYL QUANTIZATION ON
RIEMANNIAN MANIFOLDS 162 3.5 PROOF OF STRICTNESS 166 3.6 COMMUTATION
RELATIONS ON RIEMANNIAN MANIFOLDS ... 170 3.7 THE QUANTUM HAMILTONIAN
AND ITS CLASSICAL LIMIT ... 173 III GROUPS, BUNDLES, AND GROUPOIDS 178 1
LIE GROUPS AND LIE ALGEBRAS 178 1.1 LIE ALGEBRA ACTIONS AND ME MOMENTUM
MAP 178 1.2 HAMILTONIAN GROUP ACTIONS 183 1.3 MULTIPLIERS AND CENTRAL
EXTENSIONS 187 1.4 THE (TWISTED) LIE-POISSON STRUCTURE 192 1.5
PROJECTIVE REPRESENTATIONS 196 1.6 THE TWISTED ENVELOPING ALGEBRA 199
1.7 GROUP C*-ALGEBRAS 201 1.8 A GENERALIZED PETER-WEYL THEOREM 206 1.9
THE GROUP C*-ALGEBRA AS A STRICT QUANTIZATION .... 211 1.10
REPRESENTATION THEORY OF COMPACT LIE GROUPS .... 215 1.11 BEREZIN
QUANTIZATION OF COADJOINT ORBITS 219 2 INTERNAL SYMMETRIES AND EXTERNAL
GAUGE FIELDS 224 2.1 BUNDLES 224 2.2 CONNECTIONS 227 2.3 COTANGENT
BUNDLE REDUCTION 231 2.4 BUNDLE AUTOMORPHISMS AND THE GAUGE GROUP 235
2.5 CONSTRUCTION OF CLASSICAL OBSERVABLES 238 2.6 THE CLASSICAL WONG
EQUATIONS 241 2.7 THE *-CONNECTION 244 2.8 THE QUANTUM ALGEBRA OF
OBSERVABLES 249 2.9 INDUCED GROUP REPRESENTATIONS 253 2.10 THE QUANTUM
WONG HAMILTONIAN 257 2.11 FROM THE QUANTUM TO THE CLASSICAL WONG
EQUATIONS . . 260 2.12 THE DIRAC MONOPOLE 264 3 LIE GROUPOIDS AND LIE
ALGEBROIDS 269 3.1 GROUPOIDS 269 3.2 HALF-DENSITIES ON LIE GROUPOIDS 273
3.3 THE CONVOLUTION ALGEBRA OF A LIE GROUPOID 275 3.4 ACTION *-ALGEBRAS
279 3.5 REPRESENTATIONS OF GROUPOIDS 282 3.6 THE C*-ALGEBRA OF A LIE
GROUPOID 285 XVIII CONTENTS 3.7 EXAMPLES OF LIE GROUPOID C*-ALGEBRAS 288
3.8 LIE ALGEBROIDS 292 3.9 THE POISSON ALGEBRA OF A LIE ALGEBROID 296
3.10 A GENERALIZED EXPONENTIAL MAP 302 3.11 THE GROUPOID C*-ALGEBRA AS A
STRICT QUANTIZATION . . . 305 3.12 THE NORMAL GROUPOID OF A LIE GROUPOID
308 IV REDUCTION AND INDUCTION 313 1 REDUCTION 313 1.1 BASICS OF
CONSTRAINTS AND REDUCTION 313 1.2 SPECIAL SYMPLECTIC REDUCTION 316 1.3
CLASSICAL DUAL PAIRS 319 1.4 THE CLASSICAL IMPRIMITIVITY THEOREM 322 1.5
MARSDEN-WEINSTEIN REDUCTION 325 1.6 KAZHDAN-KOSTANT-STERNBERG REDUCTION
328 1.7 PROOF OF THE CLASSICAL TRANSITIVE IMPRIMITIVITY THEOREM 332 1.8
REDUCTION IN STAGES 336 1.9 COADJOINT ORBITS OF NILPOTENT GROUPS 341
1.10 COADJOINT ORBITS OF SEMIDIRECT PRODUCTS 343 1.11 SINGULAR
MARSDEN-WEINSTEIN REDUCTION 349 2 INDUCTION 354 2.1 HUBERT C*-MODULES .
354 2.2 RIEFFEL INDUCTION 358 2.3 THEC*-ALGEBRAOFAHILBERTC*-MODULE 363
2.4 THE QUANTUM IMPRIMITIVITY THEOREM 366 2.5 QUANTUM MARSDEN-WEINSTEIN
REDUCTION 370 2.6 INDUCTION IN STAGES 375 2.7 THE IMPRIMITIVITY THEOREM
FOR GAUGE GROUPOIDS . . . 378 2.8 COVARIANT QUANTIZATION 383 2.9 THE
QUANTIZATION OF CONSTRAINED SYSTEMS 386 2.10 QUANTIZATION OF SINGULAR
REDUCTION 390 3 APPLICATIONS IN RELATIVISTIC QUANTUM THEORY 393 3.1
COADJOINT ORBITS OF THE POINCARE GROUP 393 3.2 ORBITS FROM COVARIANT
REDUCTION 396 3.3 REPRESENTATIONS OF THE POINCARE GROUP 399 3.4 THE
ORIGIN OF GAUGE INVARIANCE 403 3.5 QUANTUM FIELD THEORY OF PHOTONS 407
3.6 CLASSICAL YANG-MILLS THEORY ON A CIRCLE 414 3.7 QUANTUM YANG-MILLS
THEORY ON A CIRCLE 420 3.8 INDUCTION IN QUANTUM YANG-MILLS THEORY ON A
CIRCLE . 424 3.9 VACUUM ANGLES IN CONSTRAINED QUANTIZATION 427 NOTES 433
CHAPTER 1 433 CONTENTS XIX CHAPTER II 445 CHAPTER III 457 CHAPTER IV 469
REFERENCES 483 INDEX 521
|
| any_adam_object | 1 |
| author | Landsman, Nicolaas P. |
| author_facet | Landsman, Nicolaas P. |
| author_role | aut |
| author_sort | Landsman, Nicolaas P. |
| author_variant | n p l np npl |
| building | Verbundindex |
| bvnumber | BV012421447 |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.17.M35 |
| callnumber-search | QC174.17.M35 |
| callnumber-sort | QC 3174.17 M35 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 950 UK 1200 |
| classification_tum | PHY 200f PHY 020f PHY 011f |
| ctrlnum | (OCoLC)38966087 (DE-599)BVBBV012421447 |
| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
| dewey-sort | 3530.12 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV012421447 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:27:19Z |
| institution | BVB |
| isbn | 038798318X |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008428495 |
| oclc_num | 38966087 |
| open_access_boolean | |
| owner | DE-20 DE-355 DE-BY-UBR DE-703 DE-29T DE-824 DE-384 DE-91G DE-BY-TUM DE-83 DE-11 DE-188 |
| owner_facet | DE-20 DE-355 DE-BY-UBR DE-703 DE-29T DE-824 DE-384 DE-91G DE-BY-TUM DE-83 DE-11 DE-188 |
| physical | XIX, 529 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spelling | Landsman, Nicolaas P. Verfasser aut Mathematical topics between classical and quantum mechanics N. P. Landsman New York [u.a.] Springer 1998 XIX, 529 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Champs, Théorie quantique des - Mathématique Champs, Théorie quantique des - Mathématiques ram Géométrie différentielle Géométrie différentielle ram Hilbert, Espace de Hilbert, Espaces de ram Kwantummechanica gtt Kwantumveldentheorie gtt Mecanica quantica (teoria quantica) larpcal Mécanique quantique relativiste Jussieu Observable Jussieu Physique mathématique Physique mathématique ram Quantification Jussieu Réduction Jussieu Théorie quantique - Mathématiques Théorie quantique - Mathématiques ram Mathematik Mathematische Physik Quantentheorie Geometry, Differential Hilbert space Mathematical physics Quantum field theory Mathematics Quantum theory Mathematics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s Mechanik (DE-588)4038168-7 s Mathematische Physik (DE-588)4037952-8 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008428495&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Landsman, Nicolaas P. Mathematical topics between classical and quantum mechanics Champs, Théorie quantique des - Mathématique Champs, Théorie quantique des - Mathématiques ram Géométrie différentielle Géométrie différentielle ram Hilbert, Espace de Hilbert, Espaces de ram Kwantummechanica gtt Kwantumveldentheorie gtt Mecanica quantica (teoria quantica) larpcal Mécanique quantique relativiste Jussieu Observable Jussieu Physique mathématique Physique mathématique ram Quantification Jussieu Réduction Jussieu Théorie quantique - Mathématiques Théorie quantique - Mathématiques ram Mathematik Mathematische Physik Quantentheorie Geometry, Differential Hilbert space Mathematical physics Quantum field theory Mathematics Quantum theory Mathematics Mathematische Physik (DE-588)4037952-8 gnd Mechanik (DE-588)4038168-7 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4038168-7 (DE-588)4047989-4 |
| title | Mathematical topics between classical and quantum mechanics |
| title_auth | Mathematical topics between classical and quantum mechanics |
| title_exact_search | Mathematical topics between classical and quantum mechanics |
| title_full | Mathematical topics between classical and quantum mechanics N. P. Landsman |
| title_fullStr | Mathematical topics between classical and quantum mechanics N. P. Landsman |
| title_full_unstemmed | Mathematical topics between classical and quantum mechanics N. P. Landsman |
| title_short | Mathematical topics between classical and quantum mechanics |
| title_sort | mathematical topics between classical and quantum mechanics |
| topic | Champs, Théorie quantique des - Mathématique Champs, Théorie quantique des - Mathématiques ram Géométrie différentielle Géométrie différentielle ram Hilbert, Espace de Hilbert, Espaces de ram Kwantummechanica gtt Kwantumveldentheorie gtt Mecanica quantica (teoria quantica) larpcal Mécanique quantique relativiste Jussieu Observable Jussieu Physique mathématique Physique mathématique ram Quantification Jussieu Réduction Jussieu Théorie quantique - Mathématiques Théorie quantique - Mathématiques ram Mathematik Mathematische Physik Quantentheorie Geometry, Differential Hilbert space Mathematical physics Quantum field theory Mathematics Quantum theory Mathematics Mathematische Physik (DE-588)4037952-8 gnd Mechanik (DE-588)4038168-7 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Champs, Théorie quantique des - Mathématique Champs, Théorie quantique des - Mathématiques Géométrie différentielle Hilbert, Espace de Hilbert, Espaces de Kwantummechanica Kwantumveldentheorie Mecanica quantica (teoria quantica) Mécanique quantique relativiste Observable Physique mathématique Quantification Réduction Théorie quantique - Mathématiques Mathematik Mathematische Physik Quantentheorie Geometry, Differential Hilbert space Mathematical physics Quantum field theory Mathematics Quantum theory Mathematics Mechanik Quantenmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008428495&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT landsmannicolaasp mathematicaltopicsbetweenclassicalandquantummechanics |