Domains of bosonic Functional integrals and some applications to the mathematical physics of path integrals and String Theory

TL;DR

This paper uses Minlos Theorem to rigorously define Euclidean path integrals, applying these to problems in non-linear diffusion, wave propagation, and Polyakov's path integrals, advancing mathematical physics and string theory understanding.

Contribution

It introduces new rigorous definitions of Euclidean path integrals and applies them to complex problems in mathematical physics and string theory.

Findings

Rigorous definitions of Euclidean path integrals established

Applications to non-linear diffusion and wave propagation demonstrated

New results on covariant Polyakov path integrals obtained

Abstract

By means of the Minlos Theorem on support of cylindrical measures on vectorial topological spaces, we present several results on the rigorous definitions of Euclidean path integrals and applications to some problems on non-linear diffusion, nonlinear wave propagations and covariant Polyakov"s path Integrals yielding news results on the subject as well.