Dynamical representation of the operators for the Dirac particle in the field of a plane wave
Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 1, pp. 112-123 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We find an explicit form of the integrals of motion for a Dirac particle placed in a plane-wave field. These operators are a realization of the Lie algebra of the Poincaré group in the case where the representation space consists of solutions of the Dirac–Pauli equation for the particle in a plane-wave field.
Mots-clés : Poincaré group, Dirac–Pauli equation
Keywords: Lie algebra, integral of motion, plane-wave field.
@article{TMF_2015_182_1_a6,
     author = {A. E. Lobanov},
     title = {Dynamical representation of the~operators for {the~Dirac} particle in the~field of a~plane wave},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {112--123},
     year = {2015},
     volume = {182},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_182_1_a6/}
}
TY  - JOUR
AU  - A. E. Lobanov
TI  - Dynamical representation of the operators for the Dirac particle in the field of a plane wave
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2015
SP  - 112
EP  - 123
VL  - 182
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2015_182_1_a6/
LA  - ru
ID  - TMF_2015_182_1_a6
ER  - 
%0 Journal Article
%A A. E. Lobanov
%T Dynamical representation of the operators for the Dirac particle in the field of a plane wave
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2015
%P 112-123
%V 182
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2015_182_1_a6/
%G ru
%F TMF_2015_182_1_a6
A. E. Lobanov. Dynamical representation of the operators for the Dirac particle in the field of a plane wave. Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 1, pp. 112-123. http://geodesic.mathdoc.fr/item/TMF_2015_182_1_a6/

[1] E. P. Wigner, Ann. Math. (2), 40:1 (1939), 149–204 | DOI | MR | Zbl

[2] N. N. Bogolyubov, A. A. Logunov, A. I. Oksak, I. T. Todorov, Obschie printsipy kvantovoi teorii polya, Nauka, M., 1987 | MR | MR | Zbl

[3] I. M. Gelfand, A. M. Yaglom, ZhETF, 18:8 (1948), 703–733 | MR

[4] A. Barut, R. Ronchka, Teoriya predstavlenii grupp i ee prilozheniya, Mir, M., 1980 | Zbl

[5] L. D. Landau, R. Peierls, Z. Phys., 69:1–2 (1931), 56–69 | DOI | Zbl

[6] V. G. Bagrov, D. M. Gitman, Exact Solutions of Relativistic Wave Equations, Kluwer, Dordrecht, 1990 | MR | Zbl

[7] W. Pauli, Rev. Modern Phys., 13:3 (1941), 203–232 | DOI | Zbl

[8] G. Darboux, C. R. Acad. Sci., 94 (1882), 1456–1459 | Zbl

[9] I. A. Malkin, V. I. Manko, Dinamicheskie simmetrii i kogerentnye sostoyaniya kvantovykh sistem, Nauka, M., 1979 | MR

[10] E. V. Arbuzova, A. E. Lobanov, E. M. Murchikova, Phys. Rev. D, 81:4 (2010), 045001, 16 pp., arXiv: 0903.3358 | DOI

[11] S. M. Carroll, G. B. Field, R. Jackiw, Phys. Rev. D, 41:4 (1990), 1231–1240 ; D. Colladay, V. A. Kostelecký, Phys. Rev. D, 55:11 (1997), 6760–6774, arXiv: ; D. Colladay, V. A. Kostelecký, Phys. Rev. D, 58:11 (1998), 116002, 23 pp., arXiv: ; S. Coleman, S. L. Glashow, Phys. Rev. D, 59:11 (1999), 116008, 14 pp., arXiv: hep-ph/9703464hep-ph/9809521hep-ph/9812418 | DOI | DOI | DOI | DOI

[12] F. Trev, Vvedenie v teoriyu psevdodifferentsialnykh operatorov i integralnykh operatorov Fure, Mir, M., 1984 | MR | Zbl

[13] A. Chakrabarti, Nuovo Cimento A, 56:3 (1968), 604–625 | DOI

[14] A. E. Lobanov, O. S. Pavlova, Vestnik MGU. Fizika, astr., 40:4 (1999), 3–5

[15] I. M. Ternov, V. G. Bagrov, V. A. Bordovitsyn, Yu. A. Markin, ZhETF, 52:6 (1967), 1584–1591

[16] A. E. Lobanov, Kovariantnoe opisanie spina elektrona v elektromagnitnom pole, Preprint # 24, Izd-vo MGU, M., 1988

[17] A. E. Lobanov, Vestnik MGU. Fizika, astr., 38:2 (1997), 59–60

[18] V. G. Bagrov, D. M. Gitman, M. C. Baldiotti, A. D. Levin, Ann. Phys., 14:11–12 (2006), 764–789 | DOI | MR

[19] A. S. Vshivtsev, V. Ch. Zhukovskii, A. E. Lobanov, R. A. Potapov, YaF, 57:4 (1994), 758–763

[20] D. M. Wolkow, Z. Phys., 94:3–4 (1935), 250–260 ; Д. М. Волков, ЖЭТФ, 7:11 (1937), 1286–1289 | DOI

[21] V. Bargmann, L. Michel, V. L. Telegdi, Phys. Rev. Lett., 2:10 (1959), 435–436 | DOI

[22] A. E. Lobanov, J. Phys. A, 39:23 (2006), 7517–7529, arXiv: hep-ph/0311021 | DOI | MR | Zbl

[23] A. E. Lobanov, Phys. Lett. B, 619:1–2 (2005), 136–144, arXiv: hep-ph/0506007 | DOI

[24] V. Ch. Zhukovsky, A. E. Lobanov, E. M. Murchikova, Phys. Rev. D, 73:6 (2006), 065016, 8 pp., arXiv: hep-ph/0510391 | DOI | MR

[25] A. E. Lobanov, A. I. Studenikin, Phys. Lett. B, 601:3–4 (2004), 171–175, arXiv: astro-ph/0408026 | DOI

[26] I. M. Ternov, V. G. Bagrov, A. M. Khapaev, Ann. Phys., 477:1 (1968), 25–32 | DOI | MR

[27] V. A. Bordovitsyn, I. M. Ternov, V. G. Bagrov, UFN, 165:9 (1995), 1083–1094 | DOI | DOI