Geometry, topology and quantization:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1996
|
| Schriftenreihe: | Mathematics and its applications
386 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 230 S. |
| ISBN: | 0792343050 |
Internformat
MARC
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| 100 | 1 | |a Bandyopadhyay, Pratul |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Geometry, topology and quantization |c by Pratul Bandyopadhyay |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1996 | |
| 300 | |a X, 230 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 386 | |
| 650 | 7 | |a Champs, Théorie quantique des |2 ram | |
| 650 | 7 | |a Quantification géométrique |2 ram | |
| 650 | 7 | |a Topologie |2 ram | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Geometric quantization | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Quantum field theory | |
| 650 | 4 | |a Topology | |
| 650 | 0 | 7 | |a Geometrische Quantisierung |0 (DE-588)4156720-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Geometrische Quantisierung |0 (DE-588)4156720-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Mathematics and its applications |v 386 |w (DE-604)BV008163334 |9 386 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007529743&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007529743 | ||
Datensatz im Suchindex
| _version_ | 1804125721678839808 |
|---|---|
| adam_text | Contents
Preface ix
1 Manifold and Differential Forms 1
1.1 Manifold 1
1.1.1 Topological Space 1
1.1.2 Differentiate Manifold 2
1.1.3 Hausdorff and Metric Space 3
1.1.4 Tangent and Cotangent Space 4
1.1.5 Group Manifold 6
1.2 Differential Forms 6
1.2.1 Definitions 6
1.2.2 Stokes Theorem 9
1.3 Homology and Cohomology 10
1.3.1 Simplex, Simplicial Complex and Homology 10
1.3.2 de Rham Cohomology 13
1.4 Fibre Bundles 16
1.4.1 Definitions 16
1.4.2 G Structure 19
1.4.3 Lie Derivative 19
1.4.4 Connection, Curvature and Parallel Transport 21
1.4.5 Levi Civita Connection 24
1.4.6 Bianchi Identities 25
1.4.7 Holonomy Group 27
1.5 Characteristic Classes 28
1.5.1 Definitions 28
1.5.2 Pontryagin, Euler, Chern and Stiefel Whitney Classes 29
1.5.3 Global Invariants 30
2 Spinor Structure and Twistor Geometry 35
2.1 Minkowski Space Time 35
2.1.1 Minkowski Vector Space 35
2.1.2 Lorentz and Poincare Transformation 36
2.1.3 Poincare Transformation 37
2.2 Spinors and Spin Structure 37
2.2.1 Spinor Space and Spinor Algebra 37
v
vi CONTENTS
2.2.2 Spinors and Tensors 41
2.2.3 Universal Covering Space 42
2.2.4 Spinor Structure 42
2.3 Conformal Spinors 44
2.3.1 Conformal Transformations 44
2.3.2 Spinors in E(4,2) Space 44
2.4 Supersymmetry and Superspace 47
2.4.1 Supersymmetry Algebra 47
2.4.2 Conformal Spinors, Supersymmetry and Internal Symmetry. . 49
2.4.3 Superspace 52
2.5 Twistor Geometry 53
2.5.1 Twistor Equation 53
2.5.2 Twistor Geometry, Complexified Space Time and Fermion
Number 59
2.5.3 Twistors and Cartan Semispinors 61
2.5.4 Twistor Geometry, Spinor Structure and Super space 62
3 Quantization 67
3.1 Geometric Quantization 67
3.1.1 The Quantum Condition 67
3.1.2 Prequantization 68
3.1.3 The Integrability Condition 69
3.1.4 Quantization 70
3.2 Klauder Quantization 72
3.2.1 Quantization and Coordinate Independence 72
3.2.2 Symplectic Structure and Universal Magnetic Field 78
3.2.3 Landau Levels and Geometric Quantization 79
3.3 Stochastic Quantization 81
3.3.1 Stochastic Quantization: Nelson s Approach 81
3.3.2 Stochastic Field Theory 83
3.3.3 Stochastic Quantization: Parisi Wu Approach 85
3.3.4 Stochastic Quantization and Supersymmetry 86
3.3.5 Relativistic Generalization and Quantization of a Fermi Field 87
3.3.6 Stochastic Quantization in Minkowski Space Time 91
3.3.7 Stochastic Quantization in Minkowski Space Time and Thermo
Field Dynamics 94
4 Quantization And Gauge Field 99
4.1 Equivalence of Stochastic, Klauder and Geometric Quantization ... 99
4.1.1 Stochastic Phase Space and Symplectic Structure 99
4.1.2 Role of Gauge Field 102
4.1.3 Equivalence of Different Quantization Procedures 103
4.2 Gauge Theoretic Extension 105
4.2.1 Quantization of a Fermion and SL(2,C) Gauge Structure ... 105
CONTENTS vii
4.2.2 Relativistic Quantum Particle as a Gauge Theoretic Extended
Body 108
4.2.3 SU(2) and U(l) Gauge Bundle 109
4.3 Locality and Nonlocality in Quantum Mechanics 110
4.3.1 Nonrelativistic Quantum Mechanics and Sharp Point Limit . . 110
4.3.2 Localization of a Relativistic Quantum Particle 112
4.3.3 Locality and Separability 115
4.4 Quantization and Berry Phase 116
4.4.1 The Geometric Phase 116
4.4.2 Non Abelian Geometric Phase 117
4.4.3 Non adiabatic Generalization 119
4.4.4 Classical Limit of the Geometric Phase 120
4.4.5 Topological Character of the Berry Phase 122
4.4.6 Quantization, Gauge Degrees of Freedom and Berry
Connection 124
5 Fermions and Topology 127
5.1 Quantization of a Fermion, Nonlinear Sigma Model and Vortex Line . 127
5.1.1 Bosonization: Skyrme Model 127
5.1.2 Gauge Theoretic Extension of a Fermion and Nonlinear Sigma
Model 128
5.1.3 Boson Fermion Transmutation 131
5.1.4 Vortex line, Magnetic Flux and Fermion Quantization 133
5.2 Quantization and Anomaly 137
5.2.1 Quantum Mechanical Symmetry Breaking and Anomaly . . . 137
5.2.2 Anomaly and Schwinger Term 142
5.2.3 Path Integral Formalism and Chiral Anomaly 144
5.2.4 Quantization of a Fermion and Chiral Anomaly 148
5.2.5 Quantization of a String and Conformal Anomaly 153
5.3 Anomaly and Topology 159
5.3.1 Topological Aspects of Anomaly 159
5.3.2 Chiral Anomaly and Berry Phase 170
5.3.3 Berry Phase and Fermion Number 179
6 Topological Field Theory 183
6.1 General Aspects 183
6.1.1 Definitions 183
6.1.2 Topological Field theory : Witten Type 185
6.1.3 Topological Field Theory : Schwarz Type 190
6.2 Quantization, Supersymmetry and Topological Field Theory 197
6.2.1 Topological Field Theory and Supersymmetry 197
6.2.2 Supersymmetric Sigma Model 200
6.2.3 Quantization, Supersymmetry and Topological Field Theory . 202
6.3 Geometry and Topological Field Theory 205
6.3.1 Donaldson Invariants and Topological Field Theory 205
viii CONTENTS
6.3.2 Geometry of Topological Gauge Theory 208
6.3.3 Quantization, Topological Action, and Topological Field The¬
ory in Different Dimensions 211
References 217
Index 229
|
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| dewey-full | 530.1/2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1/2 |
| dewey-search | 530.1/2 |
| dewey-sort | 3530.1 12 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV011223005 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:06:04Z |
| institution | BVB |
| isbn | 0792343050 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007529743 |
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| owner | DE-12 DE-703 DE-824 |
| owner_facet | DE-12 DE-703 DE-824 |
| physical | X, 230 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Bandyopadhyay, Pratul Verfasser aut Geometry, topology and quantization by Pratul Bandyopadhyay Dordrecht [u.a.] Kluwer 1996 X, 230 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 386 Champs, Théorie quantique des ram Quantification géométrique ram Topologie ram Mathematische Physik Geometric quantization Mathematical physics Quantum field theory Topology Geometrische Quantisierung (DE-588)4156720-1 gnd rswk-swf Geometrische Quantisierung (DE-588)4156720-1 s DE-604 Mathematics and its applications 386 (DE-604)BV008163334 386 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007529743&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bandyopadhyay, Pratul Geometry, topology and quantization Mathematics and its applications Champs, Théorie quantique des ram Quantification géométrique ram Topologie ram Mathematische Physik Geometric quantization Mathematical physics Quantum field theory Topology Geometrische Quantisierung (DE-588)4156720-1 gnd |
| subject_GND | (DE-588)4156720-1 |
| title | Geometry, topology and quantization |
| title_auth | Geometry, topology and quantization |
| title_exact_search | Geometry, topology and quantization |
| title_full | Geometry, topology and quantization by Pratul Bandyopadhyay |
| title_fullStr | Geometry, topology and quantization by Pratul Bandyopadhyay |
| title_full_unstemmed | Geometry, topology and quantization by Pratul Bandyopadhyay |
| title_short | Geometry, topology and quantization |
| title_sort | geometry topology and quantization |
| topic | Champs, Théorie quantique des ram Quantification géométrique ram Topologie ram Mathematische Physik Geometric quantization Mathematical physics Quantum field theory Topology Geometrische Quantisierung (DE-588)4156720-1 gnd |
| topic_facet | Champs, Théorie quantique des Quantification géométrique Topologie Mathematische Physik Geometric quantization Mathematical physics Quantum field theory Topology Geometrische Quantisierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007529743&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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