Geodesic
Quantization of the gravitational field in the neighborhood of the Schwarzschild solution in the relativistic theory of gravitation
Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 2, pp. 173-191 Cet article a éte moissonné depuis la source Math-Net.Ru

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Quantization of the relativistic theory of gravity [2] is performed by the method of group variables [1] in the neighbourhood of the spherically symmetric (Schwarzschild) solution for empty space. It is shown that the presence in the relativistic theory of gravity of the complete group of spatial-temporal symmetries makes it possible to remove unphysical degrees of freedom with the help of the group variables. The quantum hamiltonian is diagonalized in the quadratic approximation in the perturbing field and the formulation of boundary conditions in singular points of the background metric is investigated. Boundary conditions in the limiting singular point $r=m$ imply splitting of the space of states into the subspace of states localized in the region $r>m$ and the subspace of states localized in the region $r. States defined in the whole range of the radial variable are also constructed. Their wave functions are “continuous” (in the sense of the flux continuity) at the point $r=m$. 
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     author = {K. A. Sveshnikov and P. K. Silaev and O. A. Khrustalev},
     title = {Quantization of~the gravitational field in~the neighborhood of~the {Schwarzschild} solution in~the relativistic theory of~gravitation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1989_80_2_a1/}
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K. A. Sveshnikov; P. K. Silaev; O. A. Khrustalev. Quantization of the gravitational field in the neighborhood of the Schwarzschild solution in the relativistic theory of gravitation. Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 2, pp. 173-191. http://geodesic.mathdoc.fr/item/TMF_1989_80_2_a1/

[1] Bogolyubov N. N., UMZh, 2:2 (1950), 3–24 | MR | Zbl

[2] Logunov A. A., Mestvirishvili M. A., Osnovy relyativistskoi teorii gravitatsii, MGU, M., 1986

[3] Regge T., Nuov. Cim., 7:2 (1958), 215–219 | DOI

[4] Dirak P. A. M., Printsipy kvantovoi mekhaniki, GTTI, M., 1932 ; Боголюбов Н. Н., Ширков Д. В., Введение в теорию квантованных полей, Наука, М., 1976 | MR | MR

[5] Solovev V. O., Tverskoi V. B., Preobrazovanie Bogolyubova v relyativistskoi teorii gravitatsii, Preprint OTF 87-8, IFVE, Serpukhov, 1987

[6] Solovev V. O., Gamiltonov podkhod v relyativistskoi teorii gravitatsii i obschei teorii otnositelnosti, Preprint OTF 86-190, IFVE, Serpukhov, 1986 | MR

[7] Regge T., Wheeler J. A., Phys. Rev., 108:4 (1957), 1063–1069 ; Zerilli F. J., Phys. Rev., D2:10 (1970), 2141–2160 | DOI | MR | Zbl | MR | Zbl

[8] Price R. H., Phys. Rev., D5:10 (1972), 2439–2454 ; Chandrasekhar S., Proc. Roy. Soc., A343:2 (1975), 289–298 | MR | DOI | MR

[9] Fackerell E. D., Crossman R. G., J. Math. Phys., 18:9 (1977), 1849–1854 ; Leaver E. W., J. Math. Phys., 27:5 (1986), 1238–1265 | DOI | MR | Zbl | DOI | MR | Zbl

[10] Matzner R. A., J. Math. Phys., 9:1 (1968), 163–170 | DOI | MR

[11] Kruskal C. M., Phys. Rev., 119:8 (1960), 1743–1752 | DOI | MR

[12] Hawking S. W., Commun. Math. Phys., 43:3 (1975), 199–220 | DOI | MR | Zbl

[13] Newman E. T., Penrose R., J. Math. Phys., 7:4 (1966), 863–870 ; Goldberg J. N., Macfarlane A. J., Newman E. T., Rohrlish F., Sudarshan E. C. G., J. Math. Phys., 11 (1967), 2155–2161 | DOI | MR | DOI | MR

[14] Danford N., Shvarts Dzh. T., Lineinye operatory, Mir, M., 1966; Рихтмайер Р., Принципы современной математической физики, Мир, М., 1982 | MR

[15] Vishveshwara C. V., Phys. Rev., D1:10 (1970), 2870–2879 | MR

[16] Wald P. H., J. Math. Phys., 20:6 (1979), 1056–1058 | DOI | MR

[17] Gross D., Perry M. J., Yaffe A., Phys. Rev., D25:2 (1982), 330–355 | Zbl

[18] Razumov A. V., Preobrazovanie Bogolyubova i kvantovanie solitonov, Preprint OTF 76-52, IFVE, Serpukhov, 1976