Geodesic
Integrating Klein–Gordon–Fock equations in an external electromagnetic field on Lie groups
Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 3, pp. 375-391 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We investigate the structure of the Klein–Gordon–Fock equation symmetry algebra on pseudo-Riemannian manifolds with motions in the presence of an external electromagnetic field. We show that in the case of an invariant electromagnetic field tensor, this algebra is a one-dimensional central extension of the Lie algebra of the group of motions. Based on the coadjoint orbit method and harmonic analysis on Lie groups, we propose a method for integrating the Klein–Gordon–Fock equation in an external field on manifolds with simply transitive group actions. We consider a nontrivial example on the four-dimensional group $E(2)\times\mathbb{R}$ in detail.
Keywords: Klein–Gordon–Fock equation, symmetry operator, Lie algebra, $\lambda $-representation.
Mots-clés : Lie group 
@article{TMF_2012_173_3_a2,
     author = {A. A. Magazev},
     title = {Integrating {Klein{\textendash}Gordon{\textendash}Fock} equations in an~external electromagnetic field on {Lie} groups},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {375--391},
     year = {2012},
     volume = {173},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_173_3_a2/}
}
TY  - JOUR
AU  - A. A. Magazev
TI  - Integrating Klein–Gordon–Fock equations in an external electromagnetic field on Lie groups
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2012
SP  - 375
EP  - 391
VL  - 173
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2012_173_3_a2/
LA  - ru
ID  - TMF_2012_173_3_a2
ER  - 
%0 Journal Article
%A A. A. Magazev
%T Integrating Klein–Gordon–Fock equations in an external electromagnetic field on Lie groups
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2012
%P 375-391
%V 173
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2012_173_3_a2/
%G ru
%F TMF_2012_173_3_a2
A. A. Magazev. Integrating Klein–Gordon–Fock equations in an external electromagnetic field on Lie groups. Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 3, pp. 375-391. http://geodesic.mathdoc.fr/item/TMF_2012_173_3_a2/

[1] A. A. Grib, S. G. Mamaev, V. M. Mostepanenko, Kvantovye effekty v intensivnykh vneshnikh polyakh, Atomizdat, M., 1980

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

[3] D. V. Galtsov, Chastitsy i polya v okrestnosti chernykh dyr, Izd-vo MGU, M., 1986

[4] V. G. Bagrov, D. M. Gitman, Exact Solutions of Relativistic Wave Equations, Mathematics and Its Applications (Soviet Series), 39, Kluwer, Dordrecht, 1990 | MR | Zbl

[5] V. G. Bagrov, M. C. Baldiotti, D. M. Gitman, I. V. Shirokov, J. Math. Phys., 43:5 (2002), 2284–2305, arXiv: hep-th/0110037 | DOI | MR | Zbl

[6] A. V. Shapovalov, I. V. Shirokov, TMF, 104:2 (1995), 195–213 | DOI | MR | Zbl

[7] A. I. Breev, I. V. Shirokov, A. A. Magazev, TMF, 167:1 (2011), 78–95 | DOI | MR | Zbl

[8] S. P. Baranovskii, V. V. Mikheev, I. V. Shirokov, Izv. vuzov. Fizika, 45:11 (2002), 3–10 | MR | Zbl

[9] O. L. Kurnyavko, I. V. Shirokov, TMF, 156:2 (2008), 237–249 | DOI | MR | Zbl

[10] J. W. van Holten, Phys. Rev. Lett., 75:2 (2007), 025027, 9 pp., arXiv: hep-th/0612216 | DOI | MR

[11] M. Visinescu, Modern Phys. Lett. A, 25:5 \year 2010, 341–350, arXiv: 0910.3474 | DOI | MR | Zbl

[12] D. B. Fuks, Kogomologii beskonechnomernykh algebr Li, Nauka, M., 1984 | MR | Zbl

[13] M. Goto, F. Grosskhans, Poluprostye algebry Li, Mir, M., 1981 | MR | Zbl

[14] A. A. Magazev, I. V. Shirokov, Yu. A. Yurevich, TMF, 156:2 (2008), 189–206 | DOI | MR | Zbl

[15] A. A. Kirillov, Lektsii po metodu orbit, Nauchnaya kniga (IDMI), Novosibirsk, 2002

[16] A. A. Kirillov, Elementy teorii predstavlenii, Nauka, M., 1978 | MR

[17] M. M. Goncharovskii, I. V. Shirokov, TMF, 161:3 (2009), 332–345 | DOI | MR | Zbl

[18] Zh. Diksme, Universalnye obertyvayuschie algebry, Mir, M., 1978 | MR

[19] I. V. Shirokov, TMF, 123:3 (2000), 407–423 | DOI | MR | Zbl

[20] S. Yu. Slavyanov, V. Lai, Spetsialnye funktsii. Edinaya teoriya, osnovannaya na analize osobennostei, URSS, M., 2002 | MR | Zbl