Theoretical and Mathematical Physics

, Volume 138, Issue 3, pp 383–396

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

  • Yu. V. Pavlov

DOI: 10.1023/B:TAMP.0000018454.29920.ab

Cite this article as:
Pavlov, Y.V. Theoretical and Mathematical Physics (2004) 138: 383. doi:10.1023/B:TAMP.0000018454.29920.ab


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.

scalar field quantum theory in curved space renormalization dimensional regularization 

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • Yu. V. Pavlov
    • 1
  1. 1.Institute for Machine Engineering ProblemsRASSt. PetersburgRussia

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