Geodesic
Non-Lie integrals of the motion for particles of arbitrary spin and for systems of interacting particles
Teoretičeskaâ i matematičeskaâ fizika, Tome 88 (1991) no. 3, pp. 406-415 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

New integrals of the motion are found for the Kemmer–Duffin–Petiau, Rarita–Schwinger, Dirac–Fierz–Pauli, and Bhabha equations describing minimal and anomalous coupling of particles of spin $s\leqslant 2$ with the field of a point charge and also for a number of relativistic and quasirelativistic two- and three-particle equations. These integrals belong to the class of differential operators of order $2s$ with matrix coefficients and have a discrete spectrum. 
@article{TMF_1991_88_3_a5,
     author = {A. G. Nikitin and W. I. Fushchych},
     title = {Non-Lie integrals of the motion for particles of arbitrary spin and for systems of interacting particles},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {406--415},
     year = {1991},
     volume = {88},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_88_3_a5/}
}
TY  - JOUR
AU  - A. G. Nikitin
AU  - W. I. Fushchych
TI  - Non-Lie integrals of the motion for particles of arbitrary spin and for systems of interacting particles
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1991
SP  - 406
EP  - 415
VL  - 88
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1991_88_3_a5/
LA  - ru
ID  - TMF_1991_88_3_a5
ER  - 
%0 Journal Article
%A A. G. Nikitin
%A W. I. Fushchych
%T Non-Lie integrals of the motion for particles of arbitrary spin and for systems of interacting particles
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1991
%P 406-415
%V 88
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1991_88_3_a5/
%G ru
%F TMF_1991_88_3_a5
A. G. Nikitin; W. I. Fushchych. Non-Lie integrals of the motion for particles of arbitrary spin and for systems of interacting particles. Teoretičeskaâ i matematičeskaâ fizika, Tome 88 (1991) no. 3, pp. 406-415. http://geodesic.mathdoc.fr/item/TMF_1991_88_3_a5/

[1] Dirak P. A. M., Printsipy kvantovoi mekhaniki, Mir, M., 1979 | MR

[2] Johnson M. H., Lippman B. A., Phys. Rev., 77:3 (1950), 702 | DOI | MR | Zbl

[3] Breit G., Phys. Rev., 34:4 (1929), 553–573 | DOI | MR | Zbl

[4] Barut A. O., Komu S., Forts. Phys., 33:6 (1985), 309–318 | DOI | MR

[5] Krolikowski W., Rzewuski I., Acta Physica Polonica, 7:7 (1976), 487–496

[6] Khelashvili A. A., TMF, 51:2 (1982), 201–210

[7] Childers R. W., Phys. Rev. D, 26:10 (1982), 2902–2915 | DOI

[8] Krolikowski W., Acta Physica Polonica B, 15:10 (1984), 927–944 | MR

[9] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR

[10] Ibragimov N. Kh., Gruppy preobrazovanii v matematicheskoi fizike, Nauka, M., 1983 | MR

[11] Olver P., Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | MR | Zbl

[12] Fuschich V. I., DAN SSSR, 246:4 (1979), 846–850 | MR

[13] Fuschich V. I., Nikitin A. G., EChAYa, 14:1 (1983), 5–57 | MR

[14] Fushchich W. I., Nikitin A. G., Symmetries of Maxwell's equations, D. Reidel, Dordrecht, 1987 ; Fuschich V., Nikitin A. G., Simmetriya uravnenii Maksvella, Naukova dumka, Kiev, 1983 ; Фущич В. И., Баранник Л. Ф., Баранник А. Ф., Подгрупповая структура групп Галилея и Пуанкаре и редукция в нелинейных уравнениях, Наукова думка, Киев, 1991 | MR | Zbl | MR | MR

[15] de Amaral M. L., Zagury N., Phys. Rev. D, 26:11 (1982), 3119–3122 | DOI

[16] Fuschich V. I., Nikitin A. G., Simmetriya uravnenii kvantovoi mekhaniki, Nauka, M., 1990 | MR

[17] Stucelberg E., Helv. Phys. Acta, 11 (1938), 225

[18] Gelfand I. M., Minlos R. A., Shapiro Z. Ya., Predstavleniya gruppy vraschenii i gruppy Lorentsa, Fizmatgiz, M., 1958

[19] Rarita, Schwinger J., Phys. Rev., 60:1 (1941), 61–62 | DOI

[20] Bete G., Solpiter E., Kvantovaya mekhanika atomov s odnim i dvumya elektronami, Fizmatgiz, M., 1960

[21] Dirac P. A. M., Proc. Roy. Soc. London, A155 (1936), 447–459 | DOI

[22] Fierz M., Pauli W., Proc. Roy. Soc. London, A173 (1939), 211–232 | DOI | MR

[23] Kraicik R. A., Nieto M. M., Phys. Rev. D, 10:12 (1974), 4049–4060 | DOI | MR

[24] Levy-Leblond J.-M., Comun. Math. Phys., 6:4 (1967), 286–311 | DOI | MR | Zbl

[25] Hurley W. J., Phys. Rev. D, 3:10 (1971), 2339–2347 | DOI | MR

[26] Nikitin A. G., Fuschich V. I., TMF, 44:1 (1980), 34–46 | MR