Maslov classes, metaplectic representation and Lagrangian quantization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin
Akad.-Verl.
1997
|
| Edition: | 1. ed. |
| Series: | Mathematical research
95 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 180 - 184 |
| Physical Description: | 186 S. |
| ISBN: | 3055017145 |
Staff View
MARC
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| 245 | 1 | 0 | |a Maslov classes, metaplectic representation and Lagrangian quantization |c Maurice de Gosson |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin |b Akad.-Verl. |c 1997 | |
| 300 | |a 186 S. | ||
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| 490 | 1 | |a Mathematical research |v 95 | |
| 500 | |a Literaturverz. S. 180 - 184 | ||
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| 650 | 4 | |a Geometric quantization | |
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Record in the Search Index
| _version_ | 1804125677725679616 |
|---|---|
| adam_text | Contents
Introduction 9
Notations 14
Chapter 1. Introduction to symplectic geometry
1.1 The standard symplectic space (Z,(o) 15
1.2 The symplectic group Sp 18
1.3 The Lagrangian Grassmannian Lag of (Z,co) 24
1.4 Symplectic manifolds 28
1.5 Darboux theorem and its variants 34
1.6 State and phase space 35
1.7 Hamiltonian Mechanics in (Z,(d) 38
1.8 Hamiltonian Mechanics on symplectic manifolds 42
Comments and references 45
Chapter 2. Maslov classes
2.1 The signature of a triple of Lagrangian planes 47
2.2 The cocycle property of the signature 53
2.3 The fundamental groups of Sp and Lag 54
2.4 The index jx on Lagoo 58
2.5 Maslov Classes on Lag and Sp 64
2.6 Maslov Classes and q symplectic geometry 70
2.7 Oriented and q oriented Lagrangian manifolds 76
Comments and references 79
Chapter 3. The metaplectic representation of Sp2
3.1 The Fourier transform 81
3.2 Quadratic Fourier transforms 83
3.3 The metaplectic group Mp 90
8 Contents
3.4 Definition of the Maslov index on Mp 101
3.5 The relation between m and the Maslov index on Sp2 108
3.6 Reconstruction of the ALM index modulo 4 114
Comments and references 117
Chapter 4. Lagrangian quantization
4.1 The intrinsic Hilbert space 119
4.2 Metaplectic half forms 124
4.3 The catalogue bundle 128
4.4 Lagrangian quantization 134
Comments and references 145
Chapter 5. Quantum Mechanics
5.1 A non example of physical quantization 147
5.2 Classical interpretation of the wave function 156
5.3 The action of Hamiltonian flows onMHFs 163
5.4 Quasi classical approximation 167
5.5 Metaplectic covariance 169
Comments and references 178
Bibliography 180
Subject index 185
|
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| discipline | Physik Mathematik |
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| id | DE-604.BV011182010 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:05:22Z |
| institution | BVB |
| isbn | 3055017145 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007498833 |
| oclc_num | 36686970 |
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| physical | 186 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Akad.-Verl. |
| record_format | marc |
| series | Mathematical research |
| series2 | Mathematical research |
| spelling | Gosson, Maurice A. de 1948- Verfasser (DE-588)1024136949 aut Maslov classes, metaplectic representation and Lagrangian quantization Maurice de Gosson 1. ed. Berlin Akad.-Verl. 1997 186 S. txt rdacontent n rdamedia nc rdacarrier Mathematical research 95 Literaturverz. S. 180 - 184 Differential equations, Partial Asymptotic theory Geometric quantization Lagrangian functions Maslov index Geometrische Quantisierung (DE-588)4156720-1 gnd rswk-swf Metaplektische Darstellung (DE-588)4204500-9 gnd rswk-swf Maslov-Index (DE-588)4169023-0 gnd rswk-swf Maslov-Index (DE-588)4169023-0 s Metaplektische Darstellung (DE-588)4204500-9 s Geometrische Quantisierung (DE-588)4156720-1 s DE-604 Mathematical research 95 (DE-604)BV000008585 95 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007498833&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gosson, Maurice A. de 1948- Maslov classes, metaplectic representation and Lagrangian quantization Mathematical research Differential equations, Partial Asymptotic theory Geometric quantization Lagrangian functions Maslov index Geometrische Quantisierung (DE-588)4156720-1 gnd Metaplektische Darstellung (DE-588)4204500-9 gnd Maslov-Index (DE-588)4169023-0 gnd |
| subject_GND | (DE-588)4156720-1 (DE-588)4204500-9 (DE-588)4169023-0 |
| title | Maslov classes, metaplectic representation and Lagrangian quantization |
| title_auth | Maslov classes, metaplectic representation and Lagrangian quantization |
| title_exact_search | Maslov classes, metaplectic representation and Lagrangian quantization |
| title_full | Maslov classes, metaplectic representation and Lagrangian quantization Maurice de Gosson |
| title_fullStr | Maslov classes, metaplectic representation and Lagrangian quantization Maurice de Gosson |
| title_full_unstemmed | Maslov classes, metaplectic representation and Lagrangian quantization Maurice de Gosson |
| title_short | Maslov classes, metaplectic representation and Lagrangian quantization |
| title_sort | maslov classes metaplectic representation and lagrangian quantization |
| topic | Differential equations, Partial Asymptotic theory Geometric quantization Lagrangian functions Maslov index Geometrische Quantisierung (DE-588)4156720-1 gnd Metaplektische Darstellung (DE-588)4204500-9 gnd Maslov-Index (DE-588)4169023-0 gnd |
| topic_facet | Differential equations, Partial Asymptotic theory Geometric quantization Lagrangian functions Maslov index Geometrische Quantisierung Metaplektische Darstellung Maslov-Index |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007498833&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000008585 |
| work_keys_str_mv | AT gossonmauriceade maslovclassesmetaplecticrepresentationandlagrangianquantization |