Geodesic
The covering space method in quantum field theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 52 (1982) no. 1, pp. 51-62 
E. M. Serebryanyi. The covering space method in quantum field theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 52 (1982) no. 1, pp. 51-62. http://geodesic.mathdoc.fr/item/TMF_1982_52_1_a5/
@article{TMF_1982_52_1_a5,
     author = {E. M. Serebryanyi},
     title = {The covering space method in quantum field theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {51--62},
     year = {1982},
     volume = {52},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1982_52_1_a5/}
}
TY  - JOUR
AU  - E. M. Serebryanyi
TI  - The covering space method in quantum field theory
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1982
SP  - 51
EP  - 62
VL  - 52
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1982_52_1_a5/
LA  - ru
ID  - TMF_1982_52_1_a5
ER  - 
%0 Journal Article
%A E. M. Serebryanyi
%T The covering space method in quantum field theory
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1982
%P 51-62
%V 52
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1982_52_1_a5/
%G ru
%F TMF_1982_52_1_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

To construct the Green's function of the Laplace operator in a region $M\subset R^4$ bounded by conducting surfaces, a generalized method of images is used. It is based on replacement of the region $M$ by a discrete bundle, and therefore the expression “covering space method” is used. Transition to an imaginary value of one of the coordinates carries the Euclidean Green's function into the causal Green's function, which makes it possible (in the ease of a stable vacuum) to calculate the vacuum energy-momentum tensor of a scalar massless field.

[1] Frolov V. P., Serebriany E. M., J. Phys., A12:12 (1979), 2415–2428 | MR

[2] Frolov V. P., Serebriany E. M., J. Phys., A13:10 (1980), 3205–3211

[3] Sommerfeld A., “Über vieldeutige Potenziale in Raum”, Proc. Lond. Math. Soc., 28:13 (1897), 395–429 | Zbl

[4] Shestopal A. F., Razlozheniya po fundamentalnym resheniyam ellipticheskikh operatorov, Naukova dumka, K., 1968 | MR

[5] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya, Nauka, M., 1979 | MR

[6] Terras R., Swanson R., J. Math. Phys., 21:8 (1980), 2140–2153 | DOI | MR

[7] De Witt B. S. et al., Physica, A96:1–2 (1979), 197–211

[8] Mamaev S. G., Trunov N. N., TMF, 38:3 (1979), 345–354 | MR

[9] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Nauka, M., 1971 | MR

[10] Balian R., Duplantier B., Ann. Phys., 104:2 (1977), 300–335 ; 112:1 (1978), 165–208 | DOI | MR | DOI | MR

[11] Dowker J. S., J. Phys., A10:1 (1979), 115–124 | MR

[12] Christensen S. M., Duff M. J., Nucl. Phys., B146:1 (1978), 11–19 | DOI | MR | Zbl