Mathematical Theory of Feynman Path Integrals

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

• Publisher: Springer Berlin Heidelberg
• Year: 1976
• Tongue: English
• Leaves: 142
• Series: Lecture Notes in Mathematics 523
• Category: Library

✦ Synopsis

Feynman path integrals 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 which have occurred since then, an entire new chapter about the current forefront of research has been added. Except for this new chapter, the basic material and presentation of the first edition was mantained,  a few misprints have been corrected. At the end of each chapter the reader will also find notes with further bibliographical information.

✦ Table of Contents

Introduction....Pages 3-13
The fresnel integral of functions on a separable real Hilbert space....Pages 14-25
The Feynman path integral in potential scattering....Pages 26-45
The fresnel integral relative to a non singular quadratic form....Pages 46-64
Feynman path integrals for the anharmonic oscillator....Pages 65-79
Expectations with respect to the ground state of the harmonic oscillator....Pages 80-85
Expectations with respect to the Gibbs state of the harmonic oscillator....Pages 86-89
The invariant quasi-free states....Pages 90-104
The Feynman history integrals for the relativistic quantum boson field....Pages 105-114

✦ Subjects

Mathematics, general