Quasi-local probability averaging in the context of cutoff regularization

TL;DR

This paper investigates averaged fundamental solutions of Laplace operators using probabilistic kernels, introduces new representations, and explores implications for quantum field renormalization.

Contribution

It presents novel representations for deformed fundamental solutions and applies these to quantum field models, advancing understanding of cutoff regularization.

Findings

New representations for deformed fundamental solutions

Examples related to quantum field renormalization

Properties of averaged solutions for Laplace operators

Abstract

In this paper, we study the properties of averaged fundamental solutions of a special type for Laplace operators in the Euclidean space of an arbitrary dimension. We consider a class of kernels suitable for probabilistic averaging, and propose new representations for the deformed fundamental solutions and their values at zero. In addition, we give examples related to specific quantum field models in the context of studying renormalization properties.