Functional integration and semiclassical expansions:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Reidel
1982
|
| Series: | Mathematics and its applications
10 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 313 S. |
| ISBN: | 902771472X |
Staff View
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| 100 | 1 | |a Langouche, Flor |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Functional integration and semiclassical expansions |c F. Langouche, D. Roekaerts and E. Tirapegui |
| 264 | 1 | |a Dordrecht u.a. |b Reidel |c 1982 | |
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
Introduction xi
Chapter I : Functional integrals defined as limits of discretized expressions
1.1. Introduction 1
1.2. Definitions 5
1.3. An explicit calculation showing the discretization
dependence of the functional integral 9
1.4. Path integral from the operator formalism 13
Chapter II : Correspondence rules and functional integral representations
2.1. Correspondence between phase space functions and operators 17
2.2. Correspondence rules and discretizations 23
2.3. Equivalence classes of discretizations 28
2.4. The inverse problem 33
2.5. Determination of a correspondence rule 39
Chapter III : Functional integral representations of expectation values.
Time ordered products
3.1. Definitions 44
3.2. Representation of matrix elements by functional integrals 47
3.3. A generalized time ordered product 50
Chapter IV : Perturbation expansions
4.1. Setting up a perturbation expansion 52
4.2. Perturbation expansions and discretizations 59
4.3. Correspondence rules not satisfying n(u,0)=l 67
4.4. Extension to field theory and definition without limiting
procedure 73
Appendices 4.1 4.4 76
viii TABLE OF CONTENTS
Chapter V : Short time propagators and the relations between them
5.1. Introduction 85
5.2. On the validity of U=l ieH 86
5.3. Relations between short time propagators 93
5.4. Covariant formulation, curvature and normal coordinates 99
5.5. Short time propagator from a WKB type expansion ]04
Appendix 5.1. 115
Chapter VI : Covariant definitions of functional integrals
6.1. Introduc t ion 1 16
6.2. Feynman s definition and its generalizations 137
6.3. Graham s covariant interpretation of path integrals 120
6.4. Covariant discretizations 128
6.5. On the use of Fourier series in path integrals 132
Appendix 6.1.
Chapter VII : Functional integral methods in Fokker Planck dynamics
7.1. Introduction 139
7.2. From Langevin to Fokker Planck equation 142
7.3. Correlation and response functions 144
7.4. Perturbation expansion on arbitrary initial conditions 148
7.5. The Onsager Machlup function as Lagrangian for the most
probable path 152
7.6. Derivation of functional integral representations from
stochastic differential equations 157
Appendix 7.1 165
Chapter VIII : Product integrals
8.1. Introduction and relation with the usual functional integrals 1 67
8.2. First example: a modified Langevin equation 170
8.3. Second example: partition function of a spin 1/2 system 172
Appendix 8.1.
Chapter IX : The semiclassical expansion in phase space 185
9.1. Introduction 185
9.2. The general method 187
9.3. The covariant and gauge invariant method 197
9.4. Explicit time dependence 214
9.5. Applications 217
Appendices 9.1 9.5 228
TABLE OF CONTENTS ix
Chapter X : The semiclassical expansion in configuration space 253
10.1. Perturbation theory in configuration space 255
10.2. The free generating functional Z [j] 260
10.3. Cancellation of the singularities 269
10.A. The first order correction and the short time propagator 272
Appendices 10.1 10.2 273
Chapter XI : Other approaches 280
Chapter XII: Computation of the propagator on the sphere S 287
References 303
|
| any_adam_object | 1 |
| author | Langouche, Flor Roekaerts, Dirk Tirapegui, Enrique |
| author_facet | Langouche, Flor Roekaerts, Dirk Tirapegui, Enrique |
| author_role | aut aut aut |
| author_sort | Langouche, Flor |
| author_variant | f l fl d r dr e t et |
| building | Verbundindex |
| bvnumber | BV000042644 |
| callnumber-first | Q - Science |
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| callnumber-subject | QC - Physics |
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| dewey-ones | 530 - Physics |
| dewey-raw | 530.1/55 |
| dewey-search | 530.1/55 |
| dewey-sort | 3530.1 255 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV000042644 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:07:39Z |
| institution | BVB |
| isbn | 902771472X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000012051 |
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| physical | XII, 313 S. |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Reidel |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Langouche, Flor Verfasser aut Functional integration and semiclassical expansions F. Langouche, D. Roekaerts and E. Tirapegui Dordrecht u.a. Reidel 1982 XII, 313 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 10 Mathematische Physik Integration, Functional Mathematical physics Path integrals Funktionalintegration (DE-588)4155674-4 gnd rswk-swf Pfadintegral (DE-588)4173973-5 gnd rswk-swf Funktionalintegral (DE-588)4155673-2 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Quasiklassische Entwicklung (DE-588)4318600-2 gnd rswk-swf Quasiklassische Entwicklung (DE-588)4318600-2 s DE-604 Pfadintegral (DE-588)4173973-5 s Funktionalintegral (DE-588)4155673-2 s Funktionalintegration (DE-588)4155674-4 s Mathematische Physik (DE-588)4037952-8 s Roekaerts, Dirk Verfasser aut Tirapegui, Enrique Verfasser aut Mathematics and its applications 10 (DE-604)BV008163334 10 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000012051&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Langouche, Flor Roekaerts, Dirk Tirapegui, Enrique Functional integration and semiclassical expansions Mathematics and its applications Mathematische Physik Integration, Functional Mathematical physics Path integrals Funktionalintegration (DE-588)4155674-4 gnd Pfadintegral (DE-588)4173973-5 gnd Funktionalintegral (DE-588)4155673-2 gnd Mathematische Physik (DE-588)4037952-8 gnd Quasiklassische Entwicklung (DE-588)4318600-2 gnd |
| subject_GND | (DE-588)4155674-4 (DE-588)4173973-5 (DE-588)4155673-2 (DE-588)4037952-8 (DE-588)4318600-2 |
| title | Functional integration and semiclassical expansions |
| title_auth | Functional integration and semiclassical expansions |
| title_exact_search | Functional integration and semiclassical expansions |
| title_full | Functional integration and semiclassical expansions F. Langouche, D. Roekaerts and E. Tirapegui |
| title_fullStr | Functional integration and semiclassical expansions F. Langouche, D. Roekaerts and E. Tirapegui |
| title_full_unstemmed | Functional integration and semiclassical expansions F. Langouche, D. Roekaerts and E. Tirapegui |
| title_short | Functional integration and semiclassical expansions |
| title_sort | functional integration and semiclassical expansions |
| topic | Mathematische Physik Integration, Functional Mathematical physics Path integrals Funktionalintegration (DE-588)4155674-4 gnd Pfadintegral (DE-588)4173973-5 gnd Funktionalintegral (DE-588)4155673-2 gnd Mathematische Physik (DE-588)4037952-8 gnd Quasiklassische Entwicklung (DE-588)4318600-2 gnd |
| topic_facet | Mathematische Physik Integration, Functional Mathematical physics Path integrals Funktionalintegration Pfadintegral Funktionalintegral Quasiklassische Entwicklung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000012051&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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