Symplectic geometry and Fourier analysis:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Brookline, Mass.
Math Sci Press
1977
|
| Schriftenreihe: | Lie Groups
5 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001287773&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVII, 436 Seiten |
| ISBN: | 0915692155 |
Internformat
MARC
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| 245 | 1 | 0 | |a Symplectic geometry and Fourier analysis |c Nolan R. Wallach, Department of Mathematics, Rutgers University, New Brunswick, New Jersey |
| 264 | 1 | |a Brookline, Mass. |b Math Sci Press |c 1977 | |
| 300 | |a XVII, 436 Seiten | ||
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| 337 | |b n |2 rdamedia | ||
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| 249 | |a With an appendix on quantum mechanics |v by Robert Hermann | ||
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 430f 2001 A 35108 |
|---|---|
| DE-BY-TUM_katkey | 173104 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020025565 |
| _version_ | 1821933140395950082 |
| adam_text | TABLE OF CONTENTS
Page
PREFACE iii
Chapter 1: DIFFERENTIAL GEOMETRY 1
1. The De Rham Theorem 1
2. Line Bundles 14
3. Connections 19
Chapter 2: SYMPLECTIC GEOMETRY 39
1. Symplectic Manifolds 39
2. The Darboux Theorem 48
3. The Canonical Volume Form of a Symplectic
Manifold 56
4. The Automorphism Group of a Symplectic Manifold 58
5. Symplectic Manifolds with Integral Symplectic
Forms (Pre Quantization) 62
6. Example. T*(]Rn) 7
Chapter 3: HOMOGENEOUS SYMPLECTIC MANIFOLDS 81
1. Symplectic G Spaces 81
2. Hamiltonian G Spaces 87
3. The Classification of Homogeneous Symplectic
Manifolds 98
4. An Example 101
5. When is [wf] Integral? 108
APPENDIX TO CHAPTER 3 TORI 131
Chapter 4: FOURIER ANALYSIS 149
1. The Fourier Integral (A Rapid Review) 149
2. Tempered Distributions j°«
3. The Stone Van Neumann Theorem 1«5
4. The Irreducible Unitary Representations of the
Heisenberg Group 1
APPENDIX TO CHAPTER 4 THETA FUNCTIONS 185
xv
xvi CONTENTS
Page
Chapter 5: THE METAPLECTIC REPRESENTATION 2 05
1. The Metaplectic Group 206
2. The Symplectic Group 210
3. The Structure of the Metaplectic Group 214
4. The Metaplectic Representation 225
5. The Differential of the Metaplectic
Representation 228
6. The Hermite Functions 233
APPENDIX TO CHAPTER 5 243
Chapter 6: QUANTIZATION 255
1. Quantization 256
2. The Classical Example 258
3. Isomorphic Quantizations 263
4. The Kirillov Quantization 265
Chapter 7: THE KIRILLOV THEORY 273
1. The Heisenberg Group Revisited 273
2. Nilpotent Lie Groups 290
3. Unipotent Representation of Nilpotent Lie
Groups 297
4. Applications to the Co Adjoint Representation 305
5. The Existence of Polarizations 308
6. Unitary Representations of Nilpotent Lie
Groups 314
7. The Character Formula 334
APPENDIX I TO CHAPTER 7 TRACE CLASS OPERATORS 345
APPENDIX II TO CHAPTER 7 INDUCED REPRESENTATIONS 359
BIBLIOGRAPHY 363
CONTENTS xvii
Page
APPENDIX ON QUANTUM MECHANICS by Robert Hermann 36 7
1. Introduction 367
2. A Mathematical Model for Classical Mechanics 371
3. Conservation Laws, State and Observables for
Dynamical Systems 374
4. Observables and Conservation Laws for One
Parameter Diffeomorphism Groups on Symplectic
Manifolds 380
5. Conservation Laws, States and Observables for
Linear Symplectic Dynamical Systems 390
6. Linear Unitary Dynamical Systems 394
7. The Standard Mathematical Model for Quantum
Mechanics 400
8. The Schrbdinger and Heisenberg Equations of
Motion as a Consequence of a Choice of Lie
Algebra for the Observables 4i4
9. Further Remarks about the Problem of Quantiza
tion of a Classical Mechanical System 4/
Bibliography 435
|
| any_adam_object | 1 |
| author | Wallach, Nolan R. 1940- Hermann, Robert 1931-2020 |
| author_GND | (DE-588)133231690 (DE-588)102586333X |
| author_facet | Wallach, Nolan R. 1940- Hermann, Robert 1931-2020 |
| author_role | aut aut |
| author_sort | Wallach, Nolan R. 1940- |
| author_variant | n r w nr nrw r h rh |
| building | Verbundindex |
| bvnumber | BV001974369 |
| classification_rvk | SK 340 SK 680 |
| ctrlnum | (OCoLC)630822480 (DE-599)BVBBV001974369 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV001974369 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T07:44:07Z |
| institution | BVB |
| isbn | 0915692155 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001287773 |
| oclc_num | 630822480 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-473 DE-BY-UBG DE-703 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-706 DE-83 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-473 DE-BY-UBG DE-703 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-706 DE-83 DE-188 |
| physical | XVII, 436 Seiten |
| psigel | TUB-www |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Math Sci Press |
| record_format | marc |
| series | Lie Groups |
| series2 | Lie Groups |
| spellingShingle | Wallach, Nolan R. 1940- Hermann, Robert 1931-2020 Symplectic geometry and Fourier analysis Lie Groups Harmonische Analyse (DE-588)4023453-8 gnd Symplektische Geometrie (DE-588)4194232-2 gnd Synthetische Geometrie (DE-588)4508971-1 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4194232-2 (DE-588)4508971-1 |
| title | Symplectic geometry and Fourier analysis |
| title_alt | Appendix on quantum mechanics |
| title_auth | Symplectic geometry and Fourier analysis |
| title_exact_search | Symplectic geometry and Fourier analysis |
| title_full | Symplectic geometry and Fourier analysis Nolan R. Wallach, Department of Mathematics, Rutgers University, New Brunswick, New Jersey |
| title_fullStr | Symplectic geometry and Fourier analysis Nolan R. Wallach, Department of Mathematics, Rutgers University, New Brunswick, New Jersey |
| title_full_unstemmed | Symplectic geometry and Fourier analysis Nolan R. Wallach, Department of Mathematics, Rutgers University, New Brunswick, New Jersey |
| title_short | Symplectic geometry and Fourier analysis |
| title_sort | symplectic geometry and fourier analysis |
| topic | Harmonische Analyse (DE-588)4023453-8 gnd Symplektische Geometrie (DE-588)4194232-2 gnd Synthetische Geometrie (DE-588)4508971-1 gnd |
| topic_facet | Harmonische Analyse Symplektische Geometrie Synthetische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001287773&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001596 |
| work_keys_str_mv | AT wallachnolanr symplecticgeometryandfourieranalysis AT hermannrobert symplecticgeometryandfourieranalysis |
Inhaltsverzeichnis
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 430f 2001 A 35108 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |