Geodesic
Renormalization and Dimensional Regularization for a Scalar Field with Gauss–Bonnet-Type Coupling to Curvature
Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 2, pp. 241-255 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Yu. V. Pavlov},
     title = {Renormalization and {Dimensional} {Regularization} for {a~Scalar} {Field} with {Gauss{\textendash}Bonnet-Type} {Coupling} to {Curvature}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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Yu. V. Pavlov. Renormalization and Dimensional Regularization for a Scalar Field with Gauss–Bonnet-Type Coupling to Curvature. Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 2, pp. 241-255. http://geodesic.mathdoc.fr/item/TMF_2004_140_2_a3/

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