An introduction to symplectic geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2001
|
| Series: | Graduate studies in mathematics
26 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 195 S. graph. Darst. |
| ISBN: | 9780821820568 0821820567 |
Staff View
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Record in the Search Index
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| adam_text | AN INTRODUCTION TO SYMPLECTIC GEOMETRY ROLF BERNDT TRANSLATED BY MICHAEL
KLUCZNIK GRADUATE STUDIES IN MATHEMATICS VOLUME 26 AMERICAN MATHEMATICAL
SOCIETY PROVIDENCE, RHODE ISLAND CONTENTS PREFACE IX CHAPTER 0. SOME
ASPECTS OF THEORETICAL MECHANICS 1 §0.1. THE LAGRANGE EQUATIONS 1 §0.2.
HAMILTON S EQUATIONS 2 §0.3. THE HAMILTON-JACOBI EQUATION 4 §0.4. A
SYMPLECTIC INTERPRETATION 6 §0.5. HAMILTON S EQUATIONS VIA THE POISSON
BRACKET 6 §0.6. TOWARDS QUANTIZATION 7 CHAPTER 1. SYMPLECTIC ALGEBRA 9
§1.1. SYMPLECTIC VECTOR SPACES 9 §1.2. SYMPLECTIC MORPHISMS AND
SYMPLECTIC GROUPS 14 §1.3. SUBSPACES OF SYMPLECTIC VECTOR SPACES 17
§1.4. COMPLEX STRUCTURES OF REAL SYMPLECTIC SPACES 24 CHAPTER 2.
SYMPLECTIC MANIFOLDS 35 §2.1. SYMPLECTIC MANIFOLDS AND THEIR MORPHISMS
35 §2.2. DARBOUX S THEOREM 36 §2.3. THE COTANGENT BUNDLE 45 §2.4. KAHLER
MANIFOLDS - 45 §2.5. COADJOINT ORBITS 51 §2.6. COMPLEX PROJECTIVE SPACE
63 §2.7. SYMPLECTIC INVARIANTS (A QUICK VIEW) 68 VII VIII CONTENTS
CHAPTER 3. HAMILTONIAN VECTOR FIELDS AND THE POISSON BRACKET 71 §3.1.
PRELIMINARIES 71 §3.2. HAMILTONIAN SYSTEMS 74 §3.3. POISSON BRACKETS 79
§3.4. CONTACT MANIFOLDS 85 CHAPTER 4. THE MOMENT MAP 93 §4.1.
DEFINITIONS 93 §4.2. CONSTRUCTIONS AND EXAMPLES 97 §4.3. REDUCTION OF
PHASE SPACES BY THE CONSIDERATION OF SYMMETRY 104 CHAPTER 5.
QUANTIZATION 111 §5.1. HOMOGENEOUS QUADRATIC POLYNOMIALS AND S^ HI §5.2.
POLYNOMIALS OF DEGREE 1 AND THE HEISENBERG GROUP 114 §5.3. POLYNOMIALS
OF DEGREE 2 AND THE JACOBI GROUP 120 §5.4. THE GROENEWOLD-VAN HOVE
THEOREM 124 §5.5. TOWARDS THE GENERAL CASE 128 APPENDIX A.
DIFFERENTIABLE MANIFOLDS AND VECTOR BUNDLES 135 §A.L. DIFFERENTIABLE
MANIFOLDS AND THEIR TANGENT SPACES 135 §A.2. VECTOR BUNDLES AND THEIR
SECTIONS 144 §A.3. THE TANGENT AND THE COTANGENT BUNDLES 146 §A.4.
TENSORS AND DIFFERENTIAL FORMS 150 §A.5. CONNECTIONS 158 APPENDIX B. LIE
GROUPS AND LIE ALGEBRAS 163 §B.L. LIE ALGEBRAS AND VECTOR FIELDS 163
§B.2. LIE GROUPS AND INVARIANT VECTOR FIELDS , 165 §B.3. ONE-PARAMETER
SUBGROUPS AND THE EXPONENT MAP 167 APPENDIX C. A LITTLE COHOMOLOGY
THEORY 171 §C.L. COHOMOLOGY OF GROUPS 171 §C2. COHOMOLOGY OF LIE
ALGEBRAS 173 §C3. COHOMOLOGY OF MANIFOLDS * 174 APPENDIX D.
REPRESENTATIONS OF GROUPS 177 §D.L. LINEAR REPRESENTATIONS 177 §D.2.
CONTINUOUS AND UNITARY REPRESENTATIONS 179 §D.3. ON THE CONSTRUCTION OF
REPRESENTATIONS 180 CONTENTS BIBLIOGRAPHY 185 INDEX 189 SYMBOLS 193
|
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| language | English |
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| spelling | Berndt, Rolf Verfasser aut Einführung in die symplektische Geometrie An introduction to symplectic geometry Rolf Berndt Providence, RI American Math. Soc. 2001 XVI, 195 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 26 Symplektische Geometrie Symplektische Geometrie (DE-588)4194232-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content (DE-588)4123623-3 Lehrbuch gnd-content Symplektische Geometrie (DE-588)4194232-2 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2081-9 Graduate studies in mathematics 26 (DE-604)BV009739289 26 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009392627&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berndt, Rolf An introduction to symplectic geometry Graduate studies in mathematics Symplektische Geometrie Symplektische Geometrie (DE-588)4194232-2 gnd |
| subject_GND | (DE-588)4194232-2 (DE-588)4113937-9 (DE-588)4123623-3 |
| title | An introduction to symplectic geometry |
| title_alt | Einführung in die symplektische Geometrie |
| title_auth | An introduction to symplectic geometry |
| title_exact_search | An introduction to symplectic geometry |
| title_full | An introduction to symplectic geometry Rolf Berndt |
| title_fullStr | An introduction to symplectic geometry Rolf Berndt |
| title_full_unstemmed | An introduction to symplectic geometry Rolf Berndt |
| title_short | An introduction to symplectic geometry |
| title_sort | an introduction to symplectic geometry |
| topic | Symplektische Geometrie Symplektische Geometrie (DE-588)4194232-2 gnd |
| topic_facet | Symplektische Geometrie Hochschulschrift Lehrbuch |
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