The Euclidean Scalar Green Function in the Five-Dimensional Kaluza-Klein Magnetic Monopole Spacetime

TL;DR

This paper derives the Euclidean Green function for a massless scalar field in a five-dimensional Kaluza-Klein magnetic monopole spacetime with a global monopole, enabling analysis of vacuum polarization effects.

Contribution

It provides an integral form of the Green function in a complex higher-dimensional monopole spacetime, including contributions from different field components.

Findings

Green function expressed as sum of two contributions

Explicit calculation of renormalized vacuum expectation value

Analysis of vacuum polarization effects in the spacetime

Abstract

In this paper we present, in a integral form, the Euclidean Green function associated with a massless scalar field in the five-dimensional Kaluza-Klein magnetic monopole superposed to a global monopole, admitting a non-trivial coupling between the field with the geometry. This Green function is expressed as the sum of two contributions: the first one related with uncharged component of the field, is similar to the Green function associated with a scalar field in a four dimensional global monopole spacetime. The second contains the information of all the other components. Using this Green function it is possible to study the vacuum polarization effects on this spacetime. Explicitly we calculate the renormalized vacuum expectation value $<\Phi^*(x)\Phi(x)>_{Ren}$, which by its turn is also expressed as the sum of two contributions.