Geodesic
Forms of relativistic dynamics in a classical Lagrangian description of a system of particles
Teoretičeskaâ i matematičeskaâ fizika, Tome 55 (1983) no. 1, pp. 88-105 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The concept of a form of relativistic dynamics in the classical theory of direct interactions of particles is associated with the foliation of Minkowski space, which determines in it a simultaneity relation and makes it possible to introduce a unique evolution parameter for any set of worldlines. A three-dimensional description of a relativistic system of particles in an arbitrary form of dynamics is developed, and conditions of Poincaré invariance of the Lagrangian formalism are found. A group-theoretical classification of the possible forms of relativistic dynamics is obtained and some concrete forms of dynamics, including the instant, front, and point forms introduced by Dirac, are discussed. 
@article{TMF_1983_55_1_a8,
     author = {R. P. Gaida and Yu. B. Klyuchkovskii and V. I. Tretyak},
     title = {Forms of relativistic dynamics in a~classical {Lagrangian} description of a~system of particles},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {88--105},
     year = {1983},
     volume = {55},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_55_1_a8/}
}
TY  - JOUR
AU  - R. P. Gaida
AU  - Yu. B. Klyuchkovskii
AU  - V. I. Tretyak
TI  - Forms of relativistic dynamics in a classical Lagrangian description of a system of particles
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1983
SP  - 88
EP  - 105
VL  - 55
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1983_55_1_a8/
LA  - ru
ID  - TMF_1983_55_1_a8
ER  - 
%0 Journal Article
%A R. P. Gaida
%A Yu. B. Klyuchkovskii
%A V. I. Tretyak
%T Forms of relativistic dynamics in a classical Lagrangian description of a system of particles
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1983
%P 88-105
%V 55
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1983_55_1_a8/
%G ru
%F TMF_1983_55_1_a8
R. P. Gaida; Yu. B. Klyuchkovskii; V. I. Tretyak. Forms of relativistic dynamics in a classical Lagrangian description of a system of particles. Teoretičeskaâ i matematičeskaâ fizika, Tome 55 (1983) no. 1, pp. 88-105. http://geodesic.mathdoc.fr/item/TMF_1983_55_1_a8/

[1] Sokolov S. N., Theory of relativistic direct interactions, Preprint 78-125, IHEP, Serpukhov, 1978 | MR

[2] Gaida R. P., EChAYa, 13:2 (1982), 427–493

[3] Takabayashi T., Progr. Theor. Phys. Suppl., 1979, no. 67, 1–68 | DOI

[4] Molotkov V. V., Todorov I. T., Commun. Math. Phys., 79:1 (1981), 111–132 | DOI | MR

[5] Klepikov N. P., Shatnii A. N., TMF, 46:1 (1981), 50–63 | MR

[6] Sudarshan E. C. G., Mukunda N., Goldberg J. N., Phys. Rev., D23:10 (1981), 2218–2230 | MR

[7] Dirac P. A. M., Rev. Mod. Phys., 21:3 (1949), 392–399 | DOI | MR | Zbl

[8] Currie D. G., J. Math. Phys., 4:12 (1963), 1470–1488 | DOI | MR | Zbl

[9] Sokolov S. N., TMF, 36:2 (1978), 193–207 | MR

[10] Bel L., Ann. Inst. H. Poincare, A14:3 (1971), 189–203 | MR

[11] Gaida R. P., Klyuchkovskii Yu. B., Tretyak V. I., TMF, 44:2 (1980), 194–208 | MR

[12] Gaida R. P., Klyuchkovskii Yu. B., Tretyak V. I., TMF, 45:2 (1980), 180–198 | MR

[13] Dirak P. A. M., Lektsii po kvantovoi mekhanike, Mir, M., 1968

[14] Staruszkiewicz A., Acta Phys. Pol., B2:2–3 (1971), 259–264

[15] Medvedev B. V., Nachala teoreticheskoi fiziki, Nauka, M., 1977

[16] Sokolov S. N., Trudy Mezhdunarodnogo simpoziuma po probleme neskolkikh tel v yadernoi fizike, Dubna, 1980, 44–54

[17] Leutwyler H., Stern J., Ann. Phys. (N. Y.), 112:1 (1978), 94–164 | DOI | MR

[18] Mallik S., Hugentobler E., Phys. Rev., D20:8 (1979), 1849–1856

[19] Kondratyuk L. A., Terentev M. V., YaF, 31:4 (1980), 1087–1106 | MR

[20] Ruijsenaars S. N. M., Ann. Phys. (N. Y.), 126:2 (1980), 399–449 | DOI | MR

[21] Pauri M., Prosperi G. M., J. Math. Phys., 17:8 (1976), 1468–1495 | DOI | MR | Zbl

[22] Sokolov S. N., Relyativistskaya klassicheskaya gamiltonova mekhanika v trekh formakh dinamiki, Preprint 81-78, IFVE, Serpukhov, 1981

[23] Kogut J., Susskind L., Phys. Rep., 8:2 (1973), 75–172 | DOI

[24] Fubini S., Hanson A. J., Jackiw R., Phys. Rev., D7:6 (1973), 1732–1760

[25] Ivanitskaya O. S., Lorentsev bazis i gravitatsionnye effekty v einshteinovskoi teorii tyagoteniya, Nauka i tekhnika, Minsk, 1979 | MR

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

[27] Ibragimov N. Kh., Matem. sb., 109:2 (1979), 229–253 | MR | Zbl

[28] Currie D. G., Phys. Rev., 142:4 (1966), 817–824 | DOI | MR

[29] Patera J., Winternitz P., Zassenhaus H., J. Math. Phys., 16:8 (1975), 1597–1614 | DOI | MR | Zbl

[30] Kerner E. H., J. Math. Phys., 9:2 (1968), 222–232 | DOI | MR | Zbl