Heat-kernels and functional determinants on the generalized cone

TL;DR

This paper develops an improved method for calculating zeta functions and heat-kernel expansions on generalized cones, with detailed analysis of the global monopole case and implications for functional determinants.

Contribution

It introduces a new calculational technique for heat-kernel and zeta function analysis on generalized cones, including explicit formulas and applications to global monopoles.

Findings

Derived general formulas for heat-kernel expansions on cones

Analyzed the global monopole case in detail

Provided restrictions on the $A_{5/2}$ coefficient

Abstract

We consider zeta functions and heat-kernel expansions on the bounded, generalized cone in arbitrary dimensions using an improved calculational technique. The specific case of a global monopole is analysed in detail and some restrictions thereby placed on the $A_{5/2}$ coefficient. The computation of functional determinants is also addressed. General formulas are given and known results are incidentally, and rapidly, reproduced.