Mathematical Theory of Feynman Path Integrals An Introduction /
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...
| Main Authors: | , , |
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| Corporate Author: | |
| Language: | English |
| Published: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2008.
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| Edition: | 2nd ed. 2008. |
| Series: | Lecture Notes in Mathematics,
523 |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/978-3-540-76956-9 |
Table of Contents:
- 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.