Geodesic
On the coordinate representation in the quantum theory of gauge fields
Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 2, pp. 193-202 
I. L. Buchbinder; S. L. Lyakhovich. On the coordinate representation in the quantum theory of gauge fields. Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 2, pp. 193-202. http://geodesic.mathdoc.fr/item/TMF_1989_81_2_a3/
@article{TMF_1989_81_2_a3,
     author = {I. L. Buchbinder and S. L. Lyakhovich},
     title = {On~the coordinate representation in~the quantum theory of~gauge fields},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {193--202},
     year = {1989},
     volume = {81},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_81_2_a3/}
}
TY  - JOUR
AU  - I. L. Buchbinder
AU  - S. L. Lyakhovich
TI  - On the coordinate representation in the quantum theory of gauge fields
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1989
SP  - 193
EP  - 202
VL  - 81
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1989_81_2_a3/
LA  - ru
ID  - TMF_1989_81_2_a3
ER  - 
%0 Journal Article
%A I. L. Buchbinder
%A S. L. Lyakhovich
%T On the coordinate representation in the quantum theory of gauge fields
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1989
%P 193-202
%V 81
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1989_81_2_a3/
%G ru
%F TMF_1989_81_2_a3

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

In the general gauge theory the problem of realisation of the Hilbert space of geometrodynamical state vectors is considered. It is pointed out that the naive realization is contradictory. A consistent realization in the coordinate representation is constructed which is based on the standard canonical quantization carried out in the framework of the reduced phase space of gauge theory.

[1] Dirak P. A. M., Lektsii po kvantovoi mekhanike, Mir, M., 1969

[2] Fomin P. I., Gravitatsionnaya nestabilnost vakuuma i kosmologicheskaya problema, Preprint ITF-73-137R, ITF AN USSR, Kiev, 1973; ДАН УССР, 1975, No 9, 831–847

[3] Tryon E. P., Nature, 246 (1973), 396–399 | DOI

[4] Zeldovich Ya. B., Pisma v AZh, 7 (1981), 579–583

[5] Vilenkin A. V., Phys. Lett., 117B (1982), 25–29 | DOI | MR

[6] Linde A. D., Lett. Nuovo Cim., 39 (1984), 401–405 | DOI

[7] Uiler Dzh. A., Predvidenie Einshteina, Mir, M., 1970

[8] Grischuk L. P., Zeldovich Ya. B., Kvantovaya gravitatsiya, V. II, IYaI AN USSR, M., 1982, S. 39.

[9] Hartle J., Hawking S., Phys. Rev., D28 (1983), 2960–2972 | MR

[10] Hawking S., Nucl. Phys., B239 (1983), 257–276 | MR

[11] Hawking S., Luttrell J., Nucl. Phys., B247 (1984), 250–267 | DOI | MR

[12] Zeldovich Ya. B., Starobinskii A. A., Pisma v AZh, 10:5 (1984), 323–328

[13] Horowitz G., Phys. Rev., D31:6 (1985), 1169–1177 | MR

[14] Melnikov V. N., Pevtsov G. D., Izv. vuzov. Fiz., 1985, no. 4, 45–50 | MR

[15] Savvidi G. K., Jang–Mills quantum mechanics, Preprint ERFI No 81, ERFI, Erevan, 1984 | MR

[16] De Witt B. S., Phys. Rev., 160:5 (1967), 1113–1148 | DOI

[17] Ponomarev V. N., Barvinskii A. O., Obukhov Yu. N., Geometrodinamicheskie metody i kalibrovochnyi podkhod k teorii gravitatsionnykh vzaimodeistvii, Energoatomizdat, M., 1985 | MR

[18] Faddeev L. D., TMF, 1:1 (1969), 3–18 | MR | Zbl

[19] Fradkin E. S., Acta Universitatis Wratislaviensis, no. 207, 93–115 | MR

[20] Barwinsky A. O., Ponomariov V. N., Phys. Lett., B167 (1986), 289–293 | DOI

[21] Bukhbinder I. L., Lyakhovich S. L., O geometrodinamicheskom kvantovanii kalibrovochnykh teorii, Preprint No 20, Tomskii filial SO AN SSSR, Tomsk, 1987

[22] Kuchar K., Phys. Rev., 34:10 (1986), 3031–3043 ; 3044–3057 | MR | MR

[23] Kuchar K., Phys. Rev., D35:2 (1987), 596–599 | MR

[24] Dominici D., Gomis J., J. Math. Phys., 21:8 (1980), 2124–2130 | DOI | MR | Zbl

[25] Syndermyer K., Lect. Notes Phys., 169, 1982, 1–318 | DOI | MR

[26] Gitman D. M., Tyutin I. V., Izv. vuzov. Fiz., 1983, no. 5, 3–22 | MR

[27] Gitman D. M., Prager Ya. S., Tyutin I. V., Izv. vuzov. Fiz., 1983, no. 8, 93–97 | MR

[28] Faddeev L. D., Slavnov A. A., Vvedenie v kvantovuyu teoriyu kalibrovochnykh polei, Nauka, M., 1978 | MR | Zbl

[29] Mizner Ch., Torn K., Uiler Dzh., Gravitatsiya, t. 2, Mir, M., 1977 | MR

[30] Bukhbinder I. L., Lyakhovich S. L., TMF, 72:2 (1987), 204–218 | MR