A mathematical interpretation of the Feynman path integral equivalent to the formalism of Green functions

TL;DR

This paper introduces a rigorous mathematical framework for the Feynman path integral, showing its equivalence to Green function generating functionals through the concept of distributions on infinite-dimensional spaces.

Contribution

It formalizes the Feynman path integral as a distribution on infinite-dimensional spaces, establishing its equivalence with Green function generating functionals.

Findings

Mathematically defines distributions on infinite-dimensional spaces.

Establishes equivalence between Feynman path integrals and Green functions.

Provides a rigorous foundation for path integral formalism.

Abstract

We define the notion of distribution on an infinite dimensional space motivated by the notion of Feynman path integral and by construction of probability measures for generalized random fields. This notion of distribution turns out to be mathematically equivalent to the notion of generating functional of Green functions.