Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Pr.
1996
|
| Ausgabe: | 1. publ. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007605266&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIV, 222 S. graph. Darst. |
| ISBN: | 0521443237 |
Internformat
MARC
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| 100 | 1 | |a Guillemin, Victor |d 1937- |e Verfasser |0 (DE-588)12110172X |4 aut | |
| 245 | 1 | 0 | |a Symplectic fibrations and multiplicity diagrams |c Victor Guillemin ; Eugene Lerman ; Shlomo Sternberg |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Pr. |c 1996 | |
| 300 | |a XIV, 222 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| DE-BY-UBR_call_number | 84/SK 950 G958 S9 |
|---|---|
| DE-BY-UBR_katkey | 2286143 |
| DE-BY-UBR_location | UB Lesesaal Physik |
| DE-BY-UBR_media_number | 069022755532 |
| _version_ | 1835089957112250369 |
| adam_text | Contents
Acknowledgments poge ix
Introduction xi
1 Symplectic Fibrations 1
1.1 What Is a Symplectic Fiber Bundle? 1
1.2 Symplectic Connections 2
1.3 Minimal Coupling 5
1.4 The Coupling Form cop 7
1.5 Weak Coupling 12
1.6 Varying the Connection 17
2 Examples of Symplectic Fibrations: The Coadjoint
Orbit Hierarchy 21
2.1 Basic Example 22
2.2 A Normal Form Theorem 27
2.3 Fibrations of Coadjoint Orbits and the Cross Section Theorem 29
2.4 Symplectic Mackey Wigner Theory 45
2.5 Riemannian Submersions with Totally Geodesic Fibers 46
2.6 The Hannay Berry Connection 51
3 Duistermaat Heckman Polynomials 54
3.1 Orbital Methods in Representation Theory 54
3.2 Computing the D H Polynomials: The Case of Linear Action 65
3.3 Computing the D H Polynomials: The Heckman Formula 76
3.4 Is There a Kostant Formula Corresponding to the Heckman
Formula? 84
3.5 Computing the D H Polynomials: Formulas for the Jumps 95
v
vi Contents
Appendix 3.A: The Duistermaat Heckman Measure as the
Volume of Reduced Spaces 101
Appendix 3.B: Localization and the Duistermaat Heckman
Formula 102
4 Symplectic Fibrations and Multiplicity Diagrams 107
4.1 A Few Words about the Contents of This Chapter 107
4.2 The Heckman Formula 111
4.3 An Inductive Formula for the D H Measure Associated with a
Coadjoint Orbit of U(n) 116
4.4 The Kostant Formula 119
4.5 The Weak Coupling Limit 122
4.6 Reduction and Weak Coupling 125
4.7 Some Final Comments about Weak Coupling 130
5 Computations with Orbits 140
5.1 Generalities about Toral Moment Maps 140
5.2 Singular Values of the Moment Map O: C *¦ t 141
5.3 Examples: SU(4) Orbits 146
5.4 Duistermaat Heckman Polynomials for 10 Dimensional Orbit of
SU(4) 153
5.5 Variation of Orbits 163
Appendix A: Multiplicity Formulas 167
A.I Weyl, Kostant, and Steinberg Formulas 167
A.2 The Action of the Casimir Element on Z(k) 170
A.3 Determining the Coefficients 172
A.4 Proof of the Kostant and Weyl Formulas 175
Appendix B: Equivariant Cohomology 177
B.I Hidden Symmetries 177
B.2 Equivariant Cohomology 178
B.3 Superalgebras 180
B.4 Differential G Complexes 181
B.5 The Weil Algebra 184
B.6 The Matthai Quillen Isomorphism 186
B.7 The Cartan Model 188
B.8 Locally Free Complexes 189
B.9 Equivariant Cohomology: Homogeneous Spaces 190
B. 10 The Thorn Form According to Mattai Quillen 195
Contents vii
B.ll Equivariant Superconnections 197
B.I2 Equivariant Characteristic Classes 199
B. 13 Reduction Formula for Locally Free Torus Actions 201
B.14 Localization 204
B.15 Localization in Stages 210
Appendix C: Update 211
C.I Commutativity of Quantization and Reduction 211
C.2 Toric Varieties 213
C.3 Orbifolds 213
C.4 Presymplectic Hamiltonian Actions 214
C.5 Nonisolated Fixed Points 214
Bibliography 215
Index 221
|
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| author | Guillemin, Victor 1937- Lerman, Eugene Sternberg, Shlomo 1936- |
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| id | DE-604.BV011320006 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:10:19Z |
| institution | BVB |
| isbn | 0521443237 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007605266 |
| oclc_num | 247151868 |
| open_access_boolean | |
| owner | DE-384 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 |
| owner_facet | DE-384 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 |
| physical | XIV, 222 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Cambridge Univ. Pr. |
| record_format | marc |
| spellingShingle | Guillemin, Victor 1937- Lerman, Eugene Sternberg, Shlomo 1936- Symplectic fibrations and multiplicity diagrams Lie-Gruppe - Darstellungstheorie - Symplektische Geometrie Symplektische Geometrie (DE-588)4194232-2 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4194232-2 (DE-588)4037952-8 |
| title | Symplectic fibrations and multiplicity diagrams |
| title_auth | Symplectic fibrations and multiplicity diagrams |
| title_exact_search | Symplectic fibrations and multiplicity diagrams |
| title_full | Symplectic fibrations and multiplicity diagrams Victor Guillemin ; Eugene Lerman ; Shlomo Sternberg |
| title_fullStr | Symplectic fibrations and multiplicity diagrams Victor Guillemin ; Eugene Lerman ; Shlomo Sternberg |
| title_full_unstemmed | Symplectic fibrations and multiplicity diagrams Victor Guillemin ; Eugene Lerman ; Shlomo Sternberg |
| title_short | Symplectic fibrations and multiplicity diagrams |
| title_sort | symplectic fibrations and multiplicity diagrams |
| topic | Lie-Gruppe - Darstellungstheorie - Symplektische Geometrie Symplektische Geometrie (DE-588)4194232-2 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Lie-Gruppe - Darstellungstheorie - Symplektische Geometrie Symplektische Geometrie Mathematische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007605266&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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