On the dimensional reduced theories

TL;DR

This paper investigates the process of dimensional reduction in quantum field theories on curved space-times, specifically focusing on the partition function in warped product geometries.

Contribution

It provides a detailed analysis of how dimensional reduction affects the partition function of quantum fields in warped product curved spaces.

Findings

Derived formulas for partition functions in reduced dimensions

Clarified the role of symmetry in dimensional reduction

Identified conditions under which reduction preserves key properties

Abstract

The procedure of the dimensional reduction related to the partition function of a quantum field living in curved space-time which is the warp product of a symmetric space is investigated.