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.
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Pavlov, Y.V. The n-Wave Procedure and Dimensional Regularization for the Scalar Field in a Homogeneous Isotropic Space. Theoretical and Mathematical Physics 138, 383–396 (2004). https://doi.org/10.1023/B:TAMP.0000018454.29920.ab
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DOI: https://doi.org/10.1023/B:TAMP.0000018454.29920.ab