Convolution calculus on white noise spaces and Feynman graph representation of generalized renormalization flows

TL;DR

This paper explores innovative links between convolution calculus on white noise spaces, pseudo-differential operators, Feynman graph representations, and renormalization flows, aiming to deepen understanding of infinite-dimensional stochastic processes and particle systems.

Contribution

It introduces new connections between white noise analysis, pseudo-differential operators, and Feynman graphs in the context of renormalization group flows.

Findings

Established a novel Feynman graph representation for convolution semigroups.

Linked convolution calculus on white noise spaces with renormalization group flows.

Provided insights into the thermodynamic limit of particle systems.

Abstract

In this note we outline some novel connections between the following fields: 1) Convolution calculus on white noise spaces 2) Pseudo-differential operators and L\'evy processes on infinite dimensional spaces 3) Feynman graph representations of convolution semigroups 4) generalized renormalization group flows and 5) the thermodynamic limit of particle systems.