Dimensional renormalizability in compactified spaces

TL;DR

This paper discusses how to implement dimensional renormalization in Euclidean space-times with compactified subspaces, including effects like temperature and spatial compactification, to handle ultraviolet divergences in quantum field theories.

Contribution

It extends dimensional renormalization techniques to spaces with compactified dimensions, enabling better analysis of finite-temperature and spatially compactified quantum field theories.

Findings

Dimensional renormalization can be adapted to compactified spaces.

Techniques for handling ultraviolet divergences in these settings are outlined.

Applications include finite-temperature and spatially compactified field theories.

Abstract

We first briefly review some aspects of the techniques of dealing with ultraviolet divergences in Feynman amplitudes in an Euclidian $D$-dimensional space-time. Next we consider compactification of a $d$-dimensional ($d\leq D$) subspace. This includes effects of temperature and of compactification of $d-1$ spatial coordinates. Then we show how dimensional renormalization can be implemented for a field theory defined on this Euclidian space-time with a compactified subspace.