Mathematical Theory of Feynman Path Integrals : An Introduction / by Sergio A. Albeverio, Raphael J. Høegh-Krohn, Sonia Mazzucchi.

Format:

Book

Author/Creator:

Albeverio, Sergio, author.

Høegh-Krohn, Raphael J., author.

Mazzucchi, Sonia, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 523.

Lecture Notes in Mathematics, 0075-8434 ; 523

Language:

English

Subjects (All):

Integral equations.

Mathematics.

Functional analysis.

Operator theory.

Distribution (Probability theory).

Global analysis (Mathematics).

Integral Equations.

Measure and Integration.

Functional Analysis.

Operator Theory.

Probability Theory and Stochastic Processes.

Global Analysis and Analysis on Manifolds.

Local Subjects:

Integral Equations.

Measure and Integration.

Functional Analysis.

Operator Theory.

Probability Theory and Stochastic Processes.

Global Analysis and Analysis on Manifolds.

Physical Description:

1 online resource (X, 182 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.

System Details:

text file PDF

Summary:

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.

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.

Other Format:

Printed edition:

ISBN:

9783540769569

Access Restriction:

Restricted for use by site license.