Path integrals on group manifolds: the representation independent propagator for general Lie groups
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific Publ.
1998
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 213 S. |
| ISBN: | 9810233558 |
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MARC
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| 100 | 1 | |a Tomé, Wolfgang |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Path integrals on group manifolds |b the representation independent propagator for general Lie groups |c Wolfgang Tomé |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific Publ. |c 1998 | |
| 300 | |a XVIII, 213 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Intégrales de chemin | |
| 650 | 4 | |a Lie, Groupes de | |
| 650 | 4 | |a Variétés (Mathématiques) | |
| 650 | 4 | |a Lie groups | |
| 650 | 4 | |a Manifolds (Mathematics) | |
| 650 | 4 | |a Path integrals | |
| 650 | 0 | 7 | |a Ausbreitungsfunktion |0 (DE-588)4143498-5 |2 gnd |9 rswk-swf |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 MATHEMATICAL PRELUDE 1
1.1 Algebra 1
1.2 Functional Analysis 3
1.2.1 Operators on Hilbert Space 3
1.2.2 Direct Integrals 10
1.3 The Nuclear Spectral Theorem 17
1.3.1 Some Topological Notions 18
1.3.2 Nuclear Space 19
1.3.3 Linear Functional 23
1.3.4 Generalized Eigenvectors and the Nuclear Spectral The¬
orem 25
1.4 Lie Groups and Lie Algebras 27
1.4.1 Nilpotent, Solvable, Semisimple, and Simple Lie Algebras
and Lie Groups 30
1.4.2 The Enveloping Algebra of a Lie Algebra 31
1.5 Some Basic Notions of the Theory of Group Representation . . 32
1.5.1 Equivalence of Representations 34
1.5.2 Irreducibility of Representations 35
XV
Xvi CONTENTS
1.6 Reducible Representations 37
2 PHYSICAL PRELUDE 39
2.1 Introduction 39
2.2 The Fiducial Vector Independent Propagator for the Heisenberg
Weyl Group 42
2.2.1 Examples of the Fiducial Vector Independent Propagator 47
3 A REVIEW OF SOME MEANS TO DEFINE PATH INTE¬
GRALS ON GROUP AND SYMMETRIC SPACES 49
3.1 Feynman Path Integrals 49
3.1.1 Introduction 49
3.1.2 The Feynman Path Integral on Md 51
3.1.3 The Feynman Path Integral on Group Spaces 56
3.1.4 The Feynman Path Integral on Symmetric Spaces ... 64
3.2 Coherent State Path Integrals 73
3.2.1 Introduction 73
3.2.2 Coherent States: Minimum Requirements 74
3.2.3 Group Coherent States 75
3.2.4 Continuous Representation 77
3.2.5 The Coherent State Propagator for Group Coherent States 79
4 NOTATIONS AND PRELIMINARIES 85
4.1 Notations 85
4.2 Preliminaries 90
CONTENTS xvii
5 THE REPRESENTATION INDEPENDENT PROPAGATOR
FOR A GENERAL LIE GROUP 97
5.1 Coherent States for General Lie Groups 98
5.2 The Representation Independent Propagator for Compact Lie
Groups 106
5.3 Example: The Representation IndependentPropagator for SU(2) 113
5.3.1 The Hamilton Operator H($i,h,h) = ^js 118
5.3.2 The Hamilton Operator H{h, s2,53) = ^{s + s] + s§) 122
5.4 The Representation Independent Propagator for General Lie
Groups 125
5.4.1 Construction of the Representation Independent Propa¬
gator 125
5.4.2 Path Integral Formulation of the Representation Inde¬
pendent Propagator 133
5.5 Example: The Representation Independent Propagator for the
Affine Group 143
5.5.1 Affine Coherent States 144
5.5.2 The Representation Independent Propagator 145
6 CLASSICAL LIMIT OF THE REPRESENTATION INDE¬
PENDENT PROPAGATOR 151
6.1 Classical Limit for Compact Lie Groups 152
6.2 Classical Limit of Non Compact Lie groups 157
6.3 Classical Limit of the Representation Independent Propagator . 162
xviii CONTENTS
7 CONCLUSION AND OUTLOOK 167
7.1 Extension to Groups that do not possess square integrable, irre¬
ducible Representations 167
7.2 What has been Accomplished 171
7.3 Possible Further Directions 176
A CONTINUOUS REPRESENTATION THEORY 179
A.I Continuous Representation 179
A.2 Reproducing Kernel Hilbert Spaces 182
A.3 Proof that Equation (5.22) is Well Denned 186
B EXACT LATTICE CALCULATIONS 189
B.I The Free Particle 189
B.2 The Hamilton Operator H(Xi,X2) = ^Xf + uX2 193
BIBLIOGRAPHY 197
INDEX 209
|
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| author | Tomé, Wolfgang |
| author_facet | Tomé, Wolfgang |
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| author_sort | Tomé, Wolfgang |
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| id | DE-604.BV012875110 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:35:17Z |
| institution | BVB |
| isbn | 9810233558 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008763350 |
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| owner_facet | DE-29T DE-355 DE-BY-UBR |
| physical | XVIII, 213 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | World Scientific Publ. |
| record_format | marc |
| spelling | Tomé, Wolfgang Verfasser aut Path integrals on group manifolds the representation independent propagator for general Lie groups Wolfgang Tomé Singapore [u.a.] World Scientific Publ. 1998 XVIII, 213 S. txt rdacontent n rdamedia nc rdacarrier Intégrales de chemin Lie, Groupes de Variétés (Mathématiques) Lie groups Manifolds (Mathematics) Path integrals Ausbreitungsfunktion (DE-588)4143498-5 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Ausbreitungsfunktion (DE-588)4143498-5 s Lie-Gruppe (DE-588)4035695-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008763350&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tomé, Wolfgang Path integrals on group manifolds the representation independent propagator for general Lie groups Intégrales de chemin Lie, Groupes de Variétés (Mathématiques) Lie groups Manifolds (Mathematics) Path integrals Ausbreitungsfunktion (DE-588)4143498-5 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| subject_GND | (DE-588)4143498-5 (DE-588)4035695-4 |
| title | Path integrals on group manifolds the representation independent propagator for general Lie groups |
| title_auth | Path integrals on group manifolds the representation independent propagator for general Lie groups |
| title_exact_search | Path integrals on group manifolds the representation independent propagator for general Lie groups |
| title_full | Path integrals on group manifolds the representation independent propagator for general Lie groups Wolfgang Tomé |
| title_fullStr | Path integrals on group manifolds the representation independent propagator for general Lie groups Wolfgang Tomé |
| title_full_unstemmed | Path integrals on group manifolds the representation independent propagator for general Lie groups Wolfgang Tomé |
| title_short | Path integrals on group manifolds |
| title_sort | path integrals on group manifolds the representation independent propagator for general lie groups |
| title_sub | the representation independent propagator for general Lie groups |
| topic | Intégrales de chemin Lie, Groupes de Variétés (Mathématiques) Lie groups Manifolds (Mathematics) Path integrals Ausbreitungsfunktion (DE-588)4143498-5 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| topic_facet | Intégrales de chemin Lie, Groupes de Variétés (Mathématiques) Lie groups Manifolds (Mathematics) Path integrals Ausbreitungsfunktion Lie-Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008763350&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT tomewolfgang pathintegralsongroupmanifoldstherepresentationindependentpropagatorforgeneralliegroups |