Transfer matrices for scalar fields on curved spaces

TL;DR

This paper extends Nelson's Euclidean field construction to scalar fields on curved spaces, developing transfer matrices and analyzing their spectral properties for certain metrics, with applications to decoupling in non-convex regions.

Contribution

It introduces a method to construct transfer matrices for scalar fields on curved spaces and studies their spectral properties for specific metrics, advancing the understanding of quantum field theory in curved geometries.

Findings

Constructed transfer matrices for scalar fields on curved spaces.

Analyzed spectral properties of the transfer matrix generator.

Applied the method to decoupling in non-convex disjoint regions.

Abstract

We apply Nelson's technique of constructing Euclidean fields to the case of classical scalar fields on curved spaces. It is shown how to construct a transfer matrix and, for a class of metrics, the basic spectral properties of its generator are investigated. An application concerning decoupling of non-convex disjoint region is given.