Removal of UV cutoff for the Nelson model with variable coefficients

TL;DR

This paper investigates the Nelson model with variable coefficients, focusing on removing the ultraviolet cutoff, which is crucial for understanding the model's behavior in more general geometric settings.

Contribution

It extends the Nelson model to variable coefficients and addresses the challenging problem of ultraviolet cutoff removal in this more general context.

Findings

Successfully removed the ultraviolet cutoff for the Nelson model with variable coefficients

Established mathematical techniques for handling variable metric effects

Provided insights into the model's behavior without the cutoff

Abstract

We consider the Nelson model with variable coefficients. Nelson models with variable coefficients arise when one replaces in the usual Nelson model the flat Minkowski metric by a static metric, allowing also the boson mass to depend on position. We study the removal of the ultraviolet cutoff.