This article is cited in 8 papers

Renormalization and Dimensional Regularization for a Scalar Field with Gauss–Bonnet-Type Coupling to Curvature

Yu. V. Pavlov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences

Abstract: We consider a scalar field with a Gauss–Bonnet-type coupling to the curvature in a curved space-time. For such a quadratic coupling to the curvature, the metric energy-momentum tensor does not contain derivatives of the metric of orders greater than two. We obtain the metric energy-momentum tensor and find the geometric structure of the first three counterterms to the vacuum averages of the energy-momentum tensors for an arbitrary background metric of an $N$-dimensional space-time. In a homogeneous isotropic space, we obtain the first three counterterms of the $n$-wave procedure, which allow calculating the renormalized values of the vacuum averages of the energy-momentum tensors in the dimensions $N=4,5$. Using dimensional regularization, we establish that the geometric structures of the counterterms in the $n$-wave procedure coincide with those in the effective action method.

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

Received: 21.10.2003

DOI: 10.4213/tmf96

 English version: Theoretical and Mathematical Physics, 2004, 140:2, 1095–1108

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