Deformation quantization and index theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Akad.-Verl.
1996
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Mathematical topics
9 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 319 - 322 |
| Beschreibung: | 325 S. |
| ISBN: | 3055017161 |
Internformat
MARC
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| 100 | 1 | |a Fedosov, Boris V. |d 1938- |e Verfasser |0 (DE-588)121121879 |4 aut | |
| 245 | 1 | 0 | |a Deformation quantization and index theory |c Boris Fedosov |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin |b Akad.-Verl. |c 1996 | |
| 300 | |a 325 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical topics |v 9 | |
| 500 | |a Literaturverz. S. 319 - 322 | ||
| 650 | 7 | |a Atiyah-Singer, théorème d' |2 ram | |
| 650 | 7 | |a Groupes quantiques |2 ram | |
| 650 | 7 | |a Physique mathématique |2 ram | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Atiyah-Singer index theorem | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Perturbation groups (Mathematics) | |
| 650 | 4 | |a Quantum groups | |
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| 650 | 0 | 7 | |a Deformation |g Mathematik |0 (DE-588)4011284-6 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804124900241178624 |
|---|---|
| adam_text | Contents
1 Elements of Differential Geometry 11
1.1 Vector Bundles 11
1.2 Characteristic Classes 17
1.2.1 Connections on Vector Bundles 17
1.2.2 The Chern Weyl Theory of Characteristic Classes 24
1.3 Riemannian Manifolds 30
1.3.1 The Riemannian Connection 30
1.3.2 Homotopy Formulas 34
1.4 K Theory 37
1.4.1 K Functor with Compact Supports 37
1.4.2 The Thom Isomorphisms 43
1.5 Localization Formula 49
2 Symplectic Manifolds 52
2.1 Symplectic Spaces 52
2.2 The Hamiltonian Mechanics 56
2.3 The Darboux Theorem 60
2.4 The Generating Function 63
2.5 Symplectic Connections 66
2.6 Examples 70
3 The Weyl Quantization 76
3.1 Pseudodifferential Operators 76
3.1.1 Gaussian Integrals 76
3.1.2 Symbol Classes 80
3.2 The Composition Formula 84
3.3 Gaussian Symbols and Wave Packets 87
3.4 Operators in L2(Rn) 94
3.5 Linear Canonical Transformations 101
4 Introduction to Index Theory 110
4.1 Fredholm Operators and Families 110
4.2 Elliptic Operators 120
4.3 The Harmonic Oscillator 126
8 Contents
4.4 The Weyl Algebras Bundle 131
4.5 The Bott Generator 135
5 Deformation Quantization 138
5.1 The Formal Weyl Algebras Bundle 139
5.2 Abelian Connections and Quantization 143
5.3 Generalizations 149
5.4 The Heisenberg Equation 155
5.5 Isomorphisms of Quantum Algebras 162
5.6 Traces on Quantum Algebras 171
5.7 Poisson Manifolds 178
5.8 A Group Action 180
6 The Index Theorem for Quantum Algebras 184
6.1 Properties of the Index 184
6.2 The Thorn Isomorphism for Quantum Algebras 189
6.3 Operator Valued Coefficients 193
6.4 Formal Coefficients 201
6.5 Reordering Procedure 208
6.6 Quantum Algebras on the Total Space 221
6.7 The Case of R2n 227
6.8 The Completion of the Proof 236
7 The Asymptotic Operator Representation 240
7.1 Necessary Conditions 240
7.2 Examples 245
7.2.1 The Flag Manifold 246
7.2.2 The Projective Space 250
7.3 The Construction of the AOR 251
7.3.1 An Obstructing Cocycle 252
7.3.2 The Construction of Transition Operators 255
7.3.3 The Calculation of the Obstructing Cocycle 259
8 Symplectic Reduction 267
8.1 The Marsden Weistein Reduction 267
8.2 Quantization of the Fibering Space 271
8.3 Quantum Reduction 277
8.4 Discussion 283
9 A Trace Formula for the Schrodinger Operator 289
9.1 The Wick and Anti Wick Symbols 290
9.2 Some Estimates of Trace Norms 293
9.3 Asymptotic Solutions 295
9.4 The Wick Symbols and the AOR 299
Contents 9
9.5 A Trace Formula 304
9.6 Example 310
A Complex Symplectic Geometry 315
Bibliography 319
Index 323
|
| any_adam_object | 1 |
| author | Fedosov, Boris V. 1938- |
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| author_facet | Fedosov, Boris V. 1938- |
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| classification_rvk | SK 240 SK 350 |
| ctrlnum | (OCoLC)33971296 (DE-599)BVBBV010467090 |
| dewey-full | 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV010467090 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:53:00Z |
| institution | BVB |
| isbn | 3055017161 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006974974 |
| oclc_num | 33971296 |
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| physical | 325 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Akad.-Verl. |
| record_format | marc |
| series | Mathematical topics |
| series2 | Mathematical topics |
| spelling | Fedosov, Boris V. 1938- Verfasser (DE-588)121121879 aut Deformation quantization and index theory Boris Fedosov 1. ed. Berlin Akad.-Verl. 1996 325 S. txt rdacontent n rdamedia nc rdacarrier Mathematical topics 9 Literaturverz. S. 319 - 322 Atiyah-Singer, théorème d' ram Groupes quantiques ram Physique mathématique ram Mathematische Physik Atiyah-Singer index theorem Mathematical physics Perturbation groups (Mathematics) Quantum groups Quantisierung Physik (DE-588)4176603-9 gnd rswk-swf Indextheorie (DE-588)4161489-6 gnd rswk-swf Deformation Mathematik (DE-588)4011284-6 gnd rswk-swf Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd rswk-swf Symplektische Mannigfaltigkeit (DE-588)4290704-4 s Deformation Mathematik (DE-588)4011284-6 s Quantisierung Physik (DE-588)4176603-9 s Indextheorie (DE-588)4161489-6 s DE-604 Mathematical topics 9 (DE-604)BV008671507 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006974974&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fedosov, Boris V. 1938- Deformation quantization and index theory Mathematical topics Atiyah-Singer, théorème d' ram Groupes quantiques ram Physique mathématique ram Mathematische Physik Atiyah-Singer index theorem Mathematical physics Perturbation groups (Mathematics) Quantum groups Quantisierung Physik (DE-588)4176603-9 gnd Indextheorie (DE-588)4161489-6 gnd Deformation Mathematik (DE-588)4011284-6 gnd Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd |
| subject_GND | (DE-588)4176603-9 (DE-588)4161489-6 (DE-588)4011284-6 (DE-588)4290704-4 |
| title | Deformation quantization and index theory |
| title_auth | Deformation quantization and index theory |
| title_exact_search | Deformation quantization and index theory |
| title_full | Deformation quantization and index theory Boris Fedosov |
| title_fullStr | Deformation quantization and index theory Boris Fedosov |
| title_full_unstemmed | Deformation quantization and index theory Boris Fedosov |
| title_short | Deformation quantization and index theory |
| title_sort | deformation quantization and index theory |
| topic | Atiyah-Singer, théorème d' ram Groupes quantiques ram Physique mathématique ram Mathematische Physik Atiyah-Singer index theorem Mathematical physics Perturbation groups (Mathematics) Quantum groups Quantisierung Physik (DE-588)4176603-9 gnd Indextheorie (DE-588)4161489-6 gnd Deformation Mathematik (DE-588)4011284-6 gnd Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd |
| topic_facet | Atiyah-Singer, théorème d' Groupes quantiques Physique mathématique Mathematische Physik Atiyah-Singer index theorem Mathematical physics Perturbation groups (Mathematics) Quantum groups Quantisierung Physik Indextheorie Deformation Mathematik Symplektische Mannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006974974&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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