Vacuum Polarization Effects in the Global Monopole Spacetime in the Presence of Wu-Yang Magnetic Monopole

TL;DR

This paper investigates how Wu-Yang magnetic monopoles influence vacuum polarization effects in a global monopole spacetime, providing explicit calculations of the Green function and renormalized vacuum expectation values for a charged scalar field.

Contribution

It constructs the explicit Euclidean Green function for a charged massless scalar field in a global monopole spacetime with Wu-Yang monopoles, enabling detailed analysis of quantum effects.

Findings

Calculated the renormalized vacuum expectation value <Φ(x)^*Φ(x)>_Ren.

Derived the energy-momentum tensor <T_{μν}(x)>_Ren.

Analyzed the influence of monopoles on quantum vacuum polarization.

Abstract

In this paper we consider the presence of the Wu-Yang magnetic monopole in the global monopole spacetime and their influence on the vacuum polarization effects around these two monopoles placed together. According to Wu-Yang [Nucl. Phys. {\bf B107}, 365 (1976)] the solution of the Klein-Gordon equation in such an external field will not be an ordinary function but, instead, {\it section}. Because of the peculiar radial symmetry of the global monopole spacetime, it is possible to cover its space section by two overlapping regions, needed to define the singularity free vector potential, and to study the quantum effects due to a charged scalar field in this system. In order to develop this analysis we construct the explicit Euclidean scalar Green {\it section} associated with a charged massless field in a global monopole spacetime in the presence of the Abelian Wu-Yang magnetic monopole. Having this Green section it is possible to study the vacuum polarization effects. We explicitly calculate the renormalized vacuum expectation value $<\Phi(x)^*\Phi(x) >_{Ren.}$, associated with a charged scalar field operator and the respective energy-momentum tensor, $<T_{\mu\nu}(x)>_{Ren.}$, which are expressed in terms of the parameter which codify the presence of the global and magnetic monopoles.