Discrete heat kernel, UV modified Green's function, and higher derivative theories

TL;DR

This paper introduces a UV deformation of Green's functions in scalar field theory using a discrete heat kernel, connecting it to higher derivative theories and analyzing effects on vacuum expectations.

Contribution

It presents a novel UV deformation method based on a discrete heat kernel that recovers known effective Lagrangians and extends to higher derivative theories.

Findings

UV deformation yields Pauli-Villars effective Lagrangian

Higher derivative theories derived from UV deformation

Vacuum expectation values depend on UV cutoff

Abstract

We perform the UV deformation of the Green's function in free scalar field theory using a discrete heat kernel method. It is found that the simplest UV deformation based on the discretized diffusion equation leads to the well-known Pauli-Villars effective Lagrangian. Furthermore, by extending assumptions on the discretized equation, we find that the general higher derivative theory is derived from the present UV deformation. In some specific cases, we also calculate the vacuum expectation values of the scalar field squared in nontrivial background spaces and examine their dependence on the UV cutoff constant.