Mathematical Theory of Feynman Path Integrals

An Introduction

By: Rafael HÃ¸egh-Krohn, Sonia Mazzucchi, Sergio Albeverio

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Paperback | 30 May 2008 | Edition Number 2

At a Glance

Paperback
196 Pages

Edition Type
Revised

Dimensions(cm)
15.8 x 23.4 x 1.5

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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.

Industry Reviews

From the reviews of the second edition:

"The second edition (from 2008) contains a large additional chapter ... entitled 'Some Recent Developments', where alternative attempts at a rigourous formalism are presented, as well as recent applications. Summarizing, this is a good and insightful book for those familiar with path integrals and curious about the mathematic foundations of path integration." (Jacques Tempere, Belgian Physical Society Magazine, Issue 2, June, 2009)

"The new edition goes way beyond the habitual corrections and additions ... . It is good to have this new book. Not only for the more recent results it contains, but also as a point of departure for so many questions that are still open in the realm of infinite dimensional oscillatory integrals." (Ludwig Streit, Zentralblatt MATH, Vol. 1222, 2011)

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Preface to the Second Edition	p. V
Preface to the First Edition	p. VII
Introduction	p. 1
The Fresnel Integral of Functions on a Separable Real Hilbert Space	p. 9
The Feynman Path Integral in Potential Scattering	p. 19
The Fresnel Integral Relative to a Non-singular Quadratic Form	p. 37
Feynman Path Integrals for the Anharmonic Oscillator	p. 51
Expectations with Respect to the Ground State of the Harmonic Oscillator	p. 63
Expectations with Respect to the Gibbs State of the Harmonic Oscillator	p. 69
The Invariant Quasi-free States	p. 73
The Feynman History Integral for the Relativistic Quantum Boson Field	p. 85
Some Recent Developments	p. 93
The Infinite Dimensional Oscillatory Integral	p. 93
Feynman Path Integrals for Polynomially Growing Potentials	p. 101
The Stationary Phase Method and the Semiclassical Expansion	p. 108
Alternative Approaches to Rigorous Feynman Path Integrals	p. 115
Analytic Continuation	p. 115
White Noise Calculus Approach	p. 116
The Sequential Approach	p. 120
The Approach via Poisson Processes	p. 123
Recent Applications	p. 124
The Schrodinger Equation with Magnetic Fields	p. 124
The Schrodinger Equation with Time Dependent Potentials	p. 125
Phase Space Feynman Path Integrals	p. 130
The Stochastic Schrodinger Equation	p. 133
The Chern-Simons Functional Integral	p. 136
References of the First Edition	p. 141
References Added for the Second Edition	p. 149
Analytic Index	p. 173
List of Notations	p. 177
Table of Contents provided by Ingram. All Rights Reserved.

Mathematical Theory of Feynman Path Integrals

An Introduction

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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