Theoretical and Mathematical Physics

, Volume 128, Issue 2, pp 1034–1045 | Cite as

Dimensional Regularization and the n-Wave Procedure for Scalar Fields in Many-Dimensional Quasi-Euclidean Spaces

  • Yu. V. Pavlov


We obtain the vacuum expectation values of the energy–momentum tensor for a scalar field arbitrarily coupled to a curvature in the case of an N-dimensional quasi-Euclidean space–time; the vacuum is defined in accordance with the Hamiltonian diagonalization method. We extend the n-wave procedure to the many-dimensional case. We find all the counterterms in the case N=5 and the counterterms for the conformal scalar field in the cases N=6,7. We determine the geometric structure of the first three counterterms in the N-dimensional case. We show that all the subtractions in the four-dimensional case and the first three subtractions in the many-dimensional case correspond to the renormalization of the parameters in the bare gravitational Lagrangian. We discuss the geometric structure of the other counterterms in the many-dimensional case and the problem of eliminating the conformal anomaly in the four-dimensional case.


Scalar Field Geometric Structure Vacuum Expectation Momentum Tensor Dimensional Regularization 
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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • Yu. V. Pavlov
    • 1
  1. 1.Institute for Problems of Machine Engineering, RASSt.~PetersburgRussia

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