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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@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/}
}
TY  - JOUR
AU  - Yu. V. Pavlov
TI  - Dimensional Regularization and the $n$-Wave Procedure for Scalar Fields in Many-Dimensional Quasi-Euclidean Spaces
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2001
SP  - 236
EP  - 248
VL  - 128
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a6/
LA  - ru
ID  - TMF_2001_128_2_a6
ER  - 
%0 Journal Article
%A Yu. V. Pavlov
%T Dimensional Regularization and the $n$-Wave Procedure for Scalar Fields in Many-Dimensional Quasi-Euclidean Spaces
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2001
%P 236-248
%V 128
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a6/
%G ru
%F TMF_2001_128_2_a6
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/

[1] A. A. Grib, S. G. Mamaev, V. M. Mostepanenko, Vakuumnye kvantovye effekty v silnykh polyakh, Energoatomizdat, M., 1988

[2] N. Birrell, P. Devis, Kvantovannye polya v iskrivlennom prostranstve-vremeni, Mir, M., 1984 | MR

[3] Yu. S. Vladimirov, Razmernost fizicheskogo prostranstva-vremeni i ob'edinenie vzaimodeistvii, Izd-vo MGU, M., 1987

[4] Yu. V. Pavlov, TMF, 126:1 (2001), 115 | DOI | MR | Zbl

[5] Ya. B. Zeldovich, A. A. Starobinskii, ZhETF, 61 (1971), 2161

[6] S. G. Mamaev, V. M. Mostepanenko, V. A. Shelyuto, TMF, 63:1 (1985), 64 | MR

[7] N. A. Chernikov, E. A. Tagirov, Ann. Inst. H. Poincaré. A, 9 (1968), 109 | MR | Zbl

[8] M. Bordag, J. Lindig, V. M. Mostepanenko, Class. Quantum Grav., 15 (1998), 581 | DOI | MR | Zbl

[9] G. t'Hooft, M. Veltman, Nucl. Phys. B, 44 (1972), 189 | DOI | MR

[10] B. S. Devitt, Dinamicheskaya teoriya grupp i polei, Nauka, M., 1987 | MR

[11] V. L. Ginzburg, D. A. Kirzhnits, A. A. Lyubushin, ZhETF, 60 (1971), 451

[12] V. A. Beilin, G. M. Vereshkov, Yu. S. Grishkan i dr., ZhETF, 78 (1980), 2081 | MR