This article is cited in 6 papers

The $n$-Wave Procedure and Dimensional Regularization for the Scalar Field in a Homogeneous Isotropic Space

Yu. V. Pavlov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences

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 space correspond to a renormalization of the coupling constants of the bare gravitational Lagrangian.

Keywords: scalar field, quantum theory in curved space, renormalization, dimensional regularization.

Received: 05.06.2002
Revised: 20.03.2003

DOI: 10.4213/tmf37

 English version: Theoretical and Mathematical Physics, 2004, 138:3, 383–396

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