Vacuum polarization of scalar field on Lie groups with Bi-invariant metric

Abstract

We consider vacuum polarization of a scalar field on the Lie groups with a bi-invariant metric of Robertson-Walker type. Using the method of orbits we found expression for the vacuum expectation values of the energy-momentum tensor of the scalar field which are determined by the representation character of the group. It is shown that Einsteins equations with the energy-momentum tensor are consistent. As an example, we consider isotropic Bianchi type IX model.

Keywords

• vacuum polarization
• orbit method