Mathematical Theory of Feynman Path Integrals: An Introduction

✍ Scribed by Sergio A. Albeverio, Raphael J. Høegh-Krohn, Sonia Mazzucchi (auth.)

Publisher: Springer-Verlag Berlin Heidelberg
Year: 2008
Tongue: English
Leaves: 185
Series: Lecture Notes in Mathematics 523
Edition: 2
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-x
Introduction....Pages 1-8
The Fresnel Integral of Functions on a Separable Real Hilbert Space....Pages 9-17
The Feynman Path Integral in Potential Scattering....Pages 19-35
The Fresnel Integral Relative to a Non-singular Quadratic Form....Pages 37-50
Feynman Path Integrals for the Anharmonic Oscillator....Pages 51-62
Expectations with Respect to the Ground State of the Harmonic Oscillator....Pages 63-68
Expectations with Respect to the Gibbs State of the Harmonic Oscillator....Pages 69-71
The Invariant Quasi-free States....Pages 73-83
The Feynman History Integral for the Relativistic Quantum Boson Field....Pages 85-92
Some Recent Developments....Pages 93-140
Back Matter....Pages 141-175

✦ Subjects

Measure and Integration;Functional Analysis;Operator Theory;Probability Theory and Stochastic Processes;Global Analysis and Analysis on Manifolds;Quantum Physics

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