Geodesic
Massive neutral Dirac particle in a curved space–time with the Kerr–Schild metric
Teoretičeskaâ i matematičeskaâ fizika, Tome 125 (2000) no. 2, pp. 343-352 
D. E. Kumpyak; V. P. Tsvetkov. Massive neutral Dirac particle in a curved space–time with the Kerr–Schild metric. Teoretičeskaâ i matematičeskaâ fizika, Tome 125 (2000) no. 2, pp. 343-352. http://geodesic.mathdoc.fr/item/TMF_2000_125_2_a11/
@article{TMF_2000_125_2_a11,
     author = {D. E. Kumpyak and V. P. Tsvetkov},
     title = {Massive neutral {Dirac} particle in a curved space{\textendash}time with the {Kerr{\textendash}Schild} metric},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {343--352},
     year = {2000},
     volume = {125},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_125_2_a11/}
}
TY  - JOUR
AU  - D. E. Kumpyak
AU  - V. P. Tsvetkov
TI  - Massive neutral Dirac particle in a curved space–time with the Kerr–Schild metric
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2000
SP  - 343
EP  - 352
VL  - 125
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2000_125_2_a11/
LA  - ru
ID  - TMF_2000_125_2_a11
ER  - 
%0 Journal Article
%A D. E. Kumpyak
%A V. P. Tsvetkov
%T Massive neutral Dirac particle in a curved space–time with the Kerr–Schild metric
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2000
%P 343-352
%V 125
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2000_125_2_a11/
%G ru
%F TMF_2000_125_2_a11

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

A method for constructing the solution of the general covariant Dirac equation is developed. The solution has the form of a wave packet in the case of a slightly (compared to the wave packet size) curved space–time with the Kerr–Schild metric and describes the evolution of the spin states of a massive neutral particle with a half-integer spin. The method allows reducing the Dirac equation to a system of ordinary differential equations for the spinor amplitudes (with the necessary accuracy). We propose an iterative procedure for solving the system based on expansion with respect to a small parameter equal to the ratio between the particle wave length and the characteristic spatial scale of the change of the metric. The characteristic dissipation time of a wave packet moving in a curved space–time is estimated.

[1] Ya. B. Zeldovich, M. Yu. Khlopov, UFN, 135 (1981), 45 | DOI

[2] S. Shapiro, S. Tyukolski, Chernye dyry, belye karliki i neitronnye zvezdy, Mir, M., 1985

[3] R. P. Kerr, A. Schild, “Some algebraically degenerate solutions of Einstein's gravitational field equations”, Proc. Symp. Applied Mathematics, 17, AMS, Providence, RI, 1965, 199 | DOI | MR

[4] R. P. Kerr, Phys. Rev. Lett., 11 (1963), 237 | DOI | MR | Zbl

[5] L. D. Landau, E. M. Lifshits, Teoriya polya, Nauka, M., 1988 | MR

[6] V. P. Tsvetkov, Matem. modelirovanie, 10:2 (1998), 103

[7] V. Fock, D. Ivanenco, Zeit. Phys., 54 (1929), 798 | DOI | Zbl

[8] N. N. Bogolyubov, D. V. Shirkov, Vvedenie v teoriyu kvantovannykh polei, Nauka, M., 1976 | MR

[9] M. L. Goldberger, K. M. Vatson, Teoriya stolknovenii, Mir, M., 1967

[10] F. R. Gantmakher, Teoriya matrits, Nauka, M., 1966 | MR

[11] V. P. Tsvetkov, Izv. vuzov. Fizika, 3 (1985), 101