Mathematical Theory of Feynman Path Integrals : An Introduction / by Sergio A. Albeverio, Raphael J. Høegh-Krohn, Sonia Mazzucchi
(Lecture Notes in Mathematics ; 523)
| データ種別 | 電子ブック |
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| 出版情報 | Berlin, Heidelberg : Springer Berlin Heidelberg , 2008 |
| 本文言語 | 英語 |
| 大きさ | X, 182 p : online resource |
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| 内容注記 | Preface to the second edition Preface to the first edition 1.Introduction 2.The Fresnel Integral of Functions on a Separable Real Hilbert Spa 3.The Feynman Path Integral in Potential Scattering 4.The Fresnel Integral Relative to a Non-singular Quadratic Form 5.Feynman Path Integrals for the Anharmonic Oscillator 6.Expectations with Respect to the Ground State of the Harmonic Oscillator 7.Expectations with Respect to the Gibbs State of the Harmonic Oscillator 8.The Invariant Quasi-free States 9.The Feynman Hystory Integral for the Relativistic Quantum Boson Field 10.Some Recent Developments 10.1.The infinite dimensional oscillatory integral 10.2.Feynman path integrals for polynomially growing potentials 10.3.The semiclassical expansio 10.4.Alternative approaches to Feynman path integrals 10.4.1.Analytic continuation 10.4.2.White noise calculus 10.5.Recent applications 10.5.1.The Schroedinger equation with magnetic fields 10.5.2.The Schroedinger equation with time dependent potentials 10.5.3 .hase space Feynman path integrals 10.5.4.The stochastic Schroedinger equation 10.5.5.The Chern-Simons functional integral References of the first edition References of the second edition Analytic index List of Notations |
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| 一般注記 | Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis and geometry, and number theory. The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. To take care of the many developments since then, an entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information |
| 著者標目 | *Albeverio, Sergio A. author Høegh-Krohn, Raphael J. author Mazzucchi, Sonia author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Functional analysis LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Integral equations LCSH:Measure theory LCSH:Operator theory LCSH:Probabilities FREE:Mathematics FREE:Integral Equations FREE:Measure and Integration FREE:Functional Analysis FREE:Operator Theory FREE:Probability Theory and Stochastic Processes FREE:Global Analysis and Analysis on Manifolds |
| 分 類 | DC23:515.45 |
| 巻冊次 | ISBN:9783540769569 
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| ISBN | 9783540769569 |
| URL | http://dx.doi.org/10.1007/978-3-540-76956-9 |
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