The n-wave procedure and dimensional regularization for the scalar field in a homogeneous isotropic space

TL;DR

This paper extends the n-wave regularization method to N-dimensional homogeneous isotropic spaces, analyzing vacuum energy-momentum tensor expectations and their geometric structures using dimensional regularization.

Contribution

It generalizes the n-wave procedure to N-dimensional spaces and links subtractions in regularization to renormalization of gravitational coupling constants.

Findings

First three subtractions match between n-wave and effective action methods.

Subtractions in 4D and 5D correspond to renormalization of gravitational constants.

Geometric structures of subtractions are consistent across methods.

Abstract

We obtain expressions for the vacuum expectations of the energy-momentum tensor of the scalar field with an arbitrary coupling to the curvature in an N-dimensional homogeneous isotropic space for the vacuum determined by diagonalization of the Hamiltonian. We generalize the n-wave procedure to N-dimensional homogeneous isotropic space-time. Using the dimensional regularization, we investigate the geometric structure of the terms subtracted from the vacuum energy-momentum tensor in accordance with the n-wave procedure. We show that the geometric structures of the first three subtractions in the n-wave procedure and in the effective action method coincide. We show that all the subtractions in the n-wave procedure in a four- and five-dimensional homogeneous isotropic spaces correspond to a renormalization of the coupling constants of the bare gravitational Lagrangian.