Holdings: Geometric quantization

Geometric quantization:

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Bibliographic Details
Main Author:	Woodhouse, Nicholas M. J. 1949- (Author)
Format:	Book
Language:	English
Published:	Oxford Clarendon Press 1994
Edition:	2. ed., reprinted
Series:	Oxford mathematical monographs
Subjects:	Mathematische Methode Quantenmechanik Geometrische Quantisierung
Online Access:	Inhaltsverzeichnis
Physical Description:	XI, 307 S. graph. Darst.
ISBN:	0198536739

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MARC


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adam_text	GEOMETRIE QUANTIZATION SECOND EDITION N.M.J. WOODHOUSE MATHEMATICAL INSTITUTE UNIVERSITY OF OXFORD CLARENDON PRESS * OXFORD CONTENTS 1 SYMPLECTIC GEOMETRY 1 1.1 SYMPLECTIC MANIFOLDS 1 1.2 SYMPLECTIC VECTOR SPACES 1 1.3 THE SYMPLECTIC GROUP 5 1.4 DARBOUX S THEOREM 6 1.5 HAMILTONIAN VECTOR FIELDS 9 1.6 POISSON BRACKETS 11 1.7 SUBMANIFOLDS AND REDUCTION 12 1.8 TIME-DEPENDENT HAMILTONIANS 13 2 LAGRANGIAN AND HAMILTONIAN MECHANICS 16 2.1 HAMILTON S PRINCIPLE 16 2.2 MOMENTUM PHASE SPACE 19 2.3 THE SPACE OF MOTIONS 20 2.4 TIME-DEPENDENT LAGRANGIANS 25 2.5 CONSTRAINTS 28 2.6 TRANSFORMATIONS OF THE LAGRANGIAN 35 3 SYMMETRY 38 3.1 SYMMETRY IN QUANTUM PHYSICS 38 3.2 THE MOMENT MAP 38 3.3 THE COCYCLE CONDITION . 40 3.4 EXAMPLES 41 3.5 ELEMENTARY CLASSICAL SYSTEMS 49 3.6 DISCRETE TRANSFORMATIONS 56 3.7 MARSDEN-WEINSTEIN REDUCTION 57 4 HAMILTON-JACOBI THEORY 60 4.1 THE HAMILTON-JACOBI EQUATION 60 4.2 LAGRANGIAN SUBMANIFOLDS 61 4.3 CANONICAL TRANSFORMATIONS 62 4.4 THE TWO-POINT CHARACTERISTIC FUNCTION 64 4.5 REAL POLARIZATIONS 65 4.6 COISOTROPIC FOLIATIONS 66 4.7 GEOMETRY OF REAL POLARIZATIONS 68 4.8 POLYNOMIALS AND INVARIANT POLARIZATIONS 75 4.9 GENERATING FUNCTIONS OF REAL POLARIZATIONS 77 4.10 THE HAMILTON-JACOBI CONDITION 78 4.11 SEPARATION OF THE HAMILTON-JACOBI EQUATION 82 4.12 BIHAMILTONIAN SYSTEMS 86 CONTENTS 5 COMPLEX POLARIZATIONS 89 5.1 POLARIZATIONS AND REPRESENTATIONS 89 5.2 COMPLEX STRUCTURES 89 5.3 COMPLEX LAGRANGIAN SUBSPACES 90 5.4 COMPLEX POLARIZATIONS 92 5.5 INVARIANT POLARIZATIONS 102 6 ELEMENTARY RELATIVISTIC SYSTEMS 107 6.1 SPIN 107 6.2 TWO-COMPONENT SPINORS 107 6.3 SPINORS AND TENSORS 110 6.4 THE LORENTZ GROUP 112 6.5 ELEMENTARY RELATIVISTIC SYSTEMS 114 6.6 MASSIVE PARTICLES 115 6.7 P, C, AND T 119 6.8 MASSLESS PARTICLES 123 6.9 CLASSICAL PARTICLES IN CURVED SPACE-TIME 127 7 CLASSICAL FIELDS 130 7.1 INFINITE-DIMENSIONAL PHASE SPACES 130 7.2 THE SPACE OF SOLUTIONS 130 7.3 NOETHER S THEOREM 138 7.4 POLARIZATIONS 146 7.5 NONHYPERBOLIC EXAMPLES 152 8 PREQUANTIZATION 155 8.1 THE QUANTUM CONDITIONS 155 8.2 PREQUANTIZATION 156 8.3 THE INTEGRALITY CONDITION 158 8.4 PREQUANTIZATION OF CANONICAL TRANSFORMATIONS 162 9 QUANTIZATION 171 9.1 POLARIZATIONS AND QUANTIZATION 171 9.2 HOLOMORPHIC QUANTIZATION 173 9.3 NONNEGATIVE POLARIZATIONS 184 9.4 RELATIVISTIC QUANTIZATION 190 9.5 PAIRING 193 9.6 THE WKB APPROXIMATION 197 9.7 THE SCHROEDINGER EQUATION 201 9.8 PATH INTEGRALS AND THE FEYNMAN EXPANSION 205 9.9 PROJECTIONS AND FOCK SPACES 209 CONTENTS XI 10 THE METAPLECTIC CORRECTION 218 10.1 THE CORRECTED QUANTIZATION 218 10.2 THE METAPLECTIC REPRESENTATION 218 10.3 NONNEGATIVE LAGRANGIAN SUBSPACES 227 10.4 HALF-FORM QUANTIZATION 231 10.5 THE WKB APPROXIMATION 236 10.6 COHOMOLOGICAL WAVE FUNCTIONS 249 257 257 263 265 269 270 271 274 276 277 291 301 303 APPENDIX A.L A.2 A.3 A.4 A.5 A.6 A.7 A.8 NOTES NOTATION AND DEFINITIONS VECTOR BUNDLES LINE BUNDLES DISTRIBUTIONS AND FOLIATIONS COMPLEX MANIFOLDS COHOMOLOGY PAIRINGS AND EMBEDDINGS STATIONARY PHASE REFERENCES INDEX OF NOTATION INDEX
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author	Woodhouse, Nicholas M. J. 1949-
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indexdate	2024-07-09T18:08:17Z
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isbn	0198536739
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physical	XI, 307 S. graph. Darst.
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spelling	Woodhouse, Nicholas M. J. 1949- Verfasser (DE-588)142380253 aut Geometric quantization N. M. J. Woodhouse 2. ed., reprinted Oxford Clarendon Press 1994 XI, 307 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Geometrische Quantisierung (DE-588)4156720-1 gnd rswk-swf Geometrische Quantisierung (DE-588)4156720-1 s DE-604 Quantenmechanik (DE-588)4047989-4 s Mathematische Methode (DE-588)4155620-3 s 1\p DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007628077&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Woodhouse, Nicholas M. J. 1949- Geometric quantization Mathematische Methode (DE-588)4155620-3 gnd Quantenmechanik (DE-588)4047989-4 gnd Geometrische Quantisierung (DE-588)4156720-1 gnd
subject_GND	(DE-588)4155620-3 (DE-588)4047989-4 (DE-588)4156720-1
title	Geometric quantization
title_auth	Geometric quantization
title_exact_search	Geometric quantization
title_full	Geometric quantization N. M. J. Woodhouse
title_fullStr	Geometric quantization N. M. J. Woodhouse
title_full_unstemmed	Geometric quantization N. M. J. Woodhouse
title_short	Geometric quantization
title_sort	geometric quantization
topic	Mathematische Methode (DE-588)4155620-3 gnd Quantenmechanik (DE-588)4047989-4 gnd Geometrische Quantisierung (DE-588)4156720-1 gnd
topic_facet	Mathematische Methode Quantenmechanik Geometrische Quantisierung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007628077&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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