Path integrals, hyperbolic spaces, and Selberg trace formulae:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1996
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 280 S. |
| ISBN: | 9810224311 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804125586629591040 |
|---|---|
| adam_text | Contents
List of Tables ix
List of Figures xi
1 Introduction 1
2 Path Integrals in Quantum Mechanics 8
2.1 The Feynman Path Integral 8
2.2 Defining the Path Integral 13
2.3 Transformation Techniques 16
2.3.1 Point Canonical Transformations 16
2.3.2 Space Time Transformations 17
2.3.3 Separation of Variables 18
2.4 Group Path Integration 21
2.5 Klein Gordon Particle 24
2.6 Basic Path Integrals 25
2.6.1 The Quadratic Lagrangian 25
2.6.2 The Radial Harmonic Oscillator 26
2.6.3 The Poschl Teller Potential 26
2.6.4 The Modified Poschl Teller Potential 28
2.6.5 The 0(2, 2) Hyperboloid 29
2.6.6 Miscellaneous Results 32
3 Separable Coordinate Systems on Spaces of Constant
Curvature 34
3.1 Separation of Variables and Breaking of Symmetry. ... 34
3.2 Classification of Coordinate Systems 39
3.3 Coordinate Systems in Spaces of Constant Curvature. . . 41
V
vi CONTENTS
3.3.1 Classification of Coordinate Systems 42
3.3.2 The Sphere 44
3.3.3 Euclidean Space 44
3.3.4 The Pseudosphere 44
3.3.5 Pseudo Euclidean Space 46
3.3.6 A Hilbert Space Model 48
4 Path Integrals in Pseudo Euclidean Geometry 50
4.1 The Pseudo Euclidean Plane 50
4.2 Three Dimensional Pseudo Euclidean Space 61
5 Path Integrals in Euclidean Spaces 75
5.1 Two Dimensional Euclidean Space 75
5.2 Three Dimensional Euclidean Space 78
6 Path Integrals on Spheres 86
6.1 The Two Dimensional Sphere 86
6.2 The Three Dimensional Sphere 91
7 Path Integrals on Hyperboloids 96
7.1 The Two Dimensional Pseudosphere 96
7.2 The Three Dimensional Pseudosphere 104
8 Additional Results on Path Integration in Hyperbolic
Spaces 120
8.1 The Single Sheeted Hyperboloid 120
8.2 The /^ Dimensional Pseudosphere 122
8.3 Hyperbolic Rank One Spaces 125
9 Billiard Systems and Periodic Orbit Theory 130
9.1 Some Elements of Periodic Orbit Theory 130
9.2 A Billiard System in a Hyperbolic Rectangle 133
10 The Selberg Trace Formula 147
10.1 The Selberg Trace Formula in Mathematical Physics. . . 147
10.2 Applications and Generalizations 149
10.3 The Selberg Trace Formula on Riemann Surfaces 163
CONTENTS vii
10.3.1 The Selberg Zeta Function 171
10.3.2 Determinants of Maass Laplacians 174
10.4 The Selberg Trace Formula on Bordered Riemann Surfaces. 177
10.4.1 The Selberg Zeta Function 184
10.4.2 Determinants of Maass Laplacians 186
11 The Selberg Super Trace Formula 188
11.1 Automorphisms on Super Riemann Surfaces 188
11.1.1 Closed Super Riemann Surfaces 193
11.1.2 Compact Fundamental Domain 193
11.1.3 Non Compact Fundamental Domain 195
11.2 Selberg Super Zeta Functions 200
11.2.1 The Selberg Super Zeta Function Zo 201
11.2.2 The Selberg Super Zeta Function Z 204
11.2.3 The Selberg Super Zeta Function Zs 206
11.3 Super Determinants of Dirac Operators 208
11.4 The Selberg Super Trace Formula on Bordered Super
Riemann Surfaces 210
11.4.1 Compact Fundamental Domain 212
11.4.2 Non Compact Fundamental Domain 214
11.5 Selberg Super Zeta Functions 216
11.5.1 The Selberg Super Zeta Function Ro 217
11.5.2 The Selberg Super Zeta Function Rx 218
11.5.3 The Selberg Super Zeta Function Zs 220
11.6 Super Determinants of Dirac Operators 222
12 Summary and Discussion 224
12.1 Results on Path Integrals 224
12.2 Results on Trace Formulae 232
12.3 Miscellaneous Results, Final Remarks, and Outlook. . . . 233
Bibliography 239
Index 277
|
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| dewey-raw | 530.1/2 |
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| discipline | Physik Mathematik |
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| id | DE-604.BV011096824 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:03:55Z |
| institution | BVB |
| isbn | 9810224311 |
| language | English |
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| physical | XI, 280 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | World Scientific |
| record_format | marc |
| spelling | Grosche, Christian 1956- Verfasser (DE-588)120144913 aut Path integrals, hyperbolic spaces, and Selberg trace formulae C. Grosche Singapore [u.a.] World Scientific 1996 XI, 280 S. txt rdacontent n rdamedia nc rdacarrier Physique mathématique ram Théorie quantique ram Mathematische Physik Quantentheorie Mathematical physics Path integrals Path integrals Tables Quantum theory Selberg-Spurformel (DE-588)4248208-2 gnd rswk-swf Pfadintegral (DE-588)4173973-5 gnd rswk-swf Hyperbolischer Raum (DE-588)4161046-5 gnd rswk-swf Pfadintegral (DE-588)4173973-5 s Selberg-Spurformel (DE-588)4248208-2 s Hyperbolischer Raum (DE-588)4161046-5 s 1\p DE-604 DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007433770&sequence=000002&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 | Grosche, Christian 1956- Path integrals, hyperbolic spaces, and Selberg trace formulae Physique mathématique ram Théorie quantique ram Mathematische Physik Quantentheorie Mathematical physics Path integrals Path integrals Tables Quantum theory Selberg-Spurformel (DE-588)4248208-2 gnd Pfadintegral (DE-588)4173973-5 gnd Hyperbolischer Raum (DE-588)4161046-5 gnd |
| subject_GND | (DE-588)4248208-2 (DE-588)4173973-5 (DE-588)4161046-5 |
| title | Path integrals, hyperbolic spaces, and Selberg trace formulae |
| title_auth | Path integrals, hyperbolic spaces, and Selberg trace formulae |
| title_exact_search | Path integrals, hyperbolic spaces, and Selberg trace formulae |
| title_full | Path integrals, hyperbolic spaces, and Selberg trace formulae C. Grosche |
| title_fullStr | Path integrals, hyperbolic spaces, and Selberg trace formulae C. Grosche |
| title_full_unstemmed | Path integrals, hyperbolic spaces, and Selberg trace formulae C. Grosche |
| title_short | Path integrals, hyperbolic spaces, and Selberg trace formulae |
| title_sort | path integrals hyperbolic spaces and selberg trace formulae |
| topic | Physique mathématique ram Théorie quantique ram Mathematische Physik Quantentheorie Mathematical physics Path integrals Path integrals Tables Quantum theory Selberg-Spurformel (DE-588)4248208-2 gnd Pfadintegral (DE-588)4173973-5 gnd Hyperbolischer Raum (DE-588)4161046-5 gnd |
| topic_facet | Physique mathématique Théorie quantique Mathematische Physik Quantentheorie Mathematical physics Path integrals Path integrals Tables Quantum theory Selberg-Spurformel Pfadintegral Hyperbolischer Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007433770&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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