Vacuum polarization effects in the global monopole spacetime in the presence of the Wu-Yang magnetic monopole

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 and Yang (1976 Nucl. Phys. B 107 365) the solution of the Klein-Gordon equation in such an external field will not be an ordinary function but, instead, a 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 section associated with a charged massless field in a global monopole spacetime in the presence of the Abelian Wu-Yang magnetic monopole. Using 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-muv(x)>(Ren.), which are expressed in terms of the parameter which codifies the presence of the global and magnetic monopoles.