Geodesic
Dimensional Regularization and the $n$-Wave Procedure for Scalar Fields in Many-Dimensional Quasi-Euclidean Spaces
Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 2, pp. 236-248 
Yu. V. Pavlov. Dimensional Regularization and the $n$-Wave Procedure for Scalar Fields in Many-Dimensional Quasi-Euclidean Spaces. Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 2, pp. 236-248. http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a6/
@article{TMF_2001_128_2_a6,
     author = {Yu. V. Pavlov},
     title = {Dimensional {Regularization} and the $n${-Wave} {Procedure} for {Scalar} {Fields} in {Many-Dimensional} {Quasi-Euclidean} {Spaces}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {236--248},
     year = {2001},
     volume = {128},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a6/}
}
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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.

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