Geodesic
The $n$-Wave Procedure and Dimensional Regularization for the Scalar Field in a~Homogeneous Isotropic Space
Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 3, pp. 453-467

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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.
Keywords: scalar field, quantum theory in curved space, renormalization, dimensional regularization. 
@article{TMF_2004_138_3_a7,
     author = {Yu. V. Pavlov},
     title = {The $n${-Wave} {Procedure} and {Dimensional} {Regularization} for the {Scalar} {Field} in {a~Homogeneous} {Isotropic} {Space}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {453--467},
     publisher = {mathdoc},
     volume = {138},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_138_3_a7/}
}
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Yu. V. Pavlov. The $n$-Wave Procedure and Dimensional Regularization for the Scalar Field in a~Homogeneous Isotropic Space. Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 3, pp. 453-467. http://geodesic.mathdoc.fr/item/TMF_2004_138_3_a7/