Mathematical Feynman path integrals and their applications:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u. a.]
World Scientific
2009
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 216 S. |
| ISBN: | 9789812836908 981283690x |
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Record in the Search Index
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| adam_text | Titel: Mathematical Feynman path integrals and their applications
Autor: Mazzucchi, Sonia
Jahr: 2009
Contents
Preface v
1. Introduction 1
1.1 Wiener s and Feynman s integration............ 4
1.2 The Feynman functional................... 10
1.3 Infinite dimensional oscillatory integrals.......... 12
2. Infinite Dimensional Oscillatory Integrals 15
2.1 Finite dimensional oscillatory integrals........... 15
2.2 The Parseval type equality ................. 19
2.3 Generalized Fresnel integrals ................ 23
2.4 Infinite dimensional oscillatory integrals.......... 32
2.5 Polynomial phase functions................. 42
3. Feynman Path Integrals and the Schrodinger Equation 57
3.1 The anharmonic oscillator with a bounded anharmonic
potential............................ 57
3.2 Time dependent potentials.................. 68
3.3 Phase space Feynman path integrals............ 76
3.4 Magnetic field......................... 86
3.5 Quartic potential....................... 88
4. The Stationary Phase Method and the Semiclassical
Limit of Quantum Mechanics 101
4.1 Asymptotic expansions.................... 101
4.2 The stationary phase method. Finite dimensional case . . 106
viii Mathematical Feynman Path Integrals and Applications
4.3 The stationary phase method. Infinite dimensional case . 115
4.4 The semiclassical limit of quantum mechanics....... 128
4.5 The trace formula ...................... 138
5. Open Quantum Systems 147
5.1 Feynman path integrals and open quantum systems . . . 147
5.2 The Feynman-Vernon influence functional......... 155
5.3 The stochastic Schrodinger equation............ 165
6- Alternative Approaches to Feynman Path Integration 177
6.1 Analytic continuation of Wiener integrals......... 177
6.2 The sequential approach................... 181
6.3 White noise calculus..................... 184
6.4 Poisson processes....................... 188
6.5 Further approaches and results............... 189
Appendix A Abstract Wiener Spaces 191
A.I General theory........................ 191
A.2 The classical Wiener space.................. 195
Bibliography 197
Index 215
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| spelling | Mazzucchi, Sonia Verfasser aut Mathematical Feynman path integrals and their applications Sonia Mazzucchi New Jersey [u. a.] World Scientific 2009 VIII, 216 S. txt rdacontent n rdamedia nc rdacarrier Pfadintegral (DE-588)4173973-5 gnd rswk-swf Pfadintegral (DE-588)4173973-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018606875&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mazzucchi, Sonia Mathematical Feynman path integrals and their applications Pfadintegral (DE-588)4173973-5 gnd |
| subject_GND | (DE-588)4173973-5 |
| title | Mathematical Feynman path integrals and their applications |
| title_auth | Mathematical Feynman path integrals and their applications |
| title_exact_search | Mathematical Feynman path integrals and their applications |
| title_full | Mathematical Feynman path integrals and their applications Sonia Mazzucchi |
| title_fullStr | Mathematical Feynman path integrals and their applications Sonia Mazzucchi |
| title_full_unstemmed | Mathematical Feynman path integrals and their applications Sonia Mazzucchi |
| title_short | Mathematical Feynman path integrals and their applications |
| title_sort | mathematical feynman path integrals and their applications |
| topic | Pfadintegral (DE-588)4173973-5 gnd |
| topic_facet | Pfadintegral |
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