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Integral Transforms and Special Functions

Integral transform as operator-valued Feynman integrals via conditional Feynman integrals over Wiener paths in abstract Wiener space

Dong Hyun Cho

Published Feb 15, 2005• 1 citation
Publisher

Abstract

In this article, we introduce an integral transform as operator-valued Feynman integrals over Wiener paths in abstract Wiener space. In addition, we evaluate the integral transform for various types of functions, which are of interest in quantum mechanics and Feynman integration theories, via the conditional Feynman integral over Wiener paths in abstract Wiener space as a kernel.

DOI
10.1080/10652460410001672988

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In this article, we introduce an integral transform as operator-valued Feynman integrals over Wiener paths in abstract Wiener space. In addition, we evaluate the integral transform for various types of functions, which are of interest in quantum mechanics and Feynman integration theories, via the conditional Feynman integral over Wiener paths in abstract Wiener space as a kernel.
This translation of the survey article by I. M. Gel'fand and A. M. Yaglom on the theory and applications of integration in functional spaces in problems of quantum physics was prepared because it was felt that such a review would be of interest and of use to mathematical physicists working in several different fields. The article begins with a discussion of Wiener measure, after which the extension is made to the complex measure introduced by Feynman in his formulation of quantum mechanics, and examples are given of the use of these methods in quantum mechanics, quantum field theory, and quantum statistical physics. A comprehensive bibliography of works devoted to the theory and applications of functional integration methods is included.