Geodesic
Formulation of the relativistic mechanics of systems of interacting particles
Teoretičeskaâ i matematičeskaâ fizika, Tome 46 (1981) no. 1, pp. 50-63 Cet article a éte moissonné depuis la source Math-Net.Ru

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A Poincaré invariant formulation of classical relativistic mechanics of a system of $n$ interacting particles is given. The equations of motion are the equations of the characteristics of a Pfaffian form, which relates the action element to the elements of the $4n$ coordinates of the system. The characteristics are found on a subsurface defined by $n$ constraints, which include the particle masses. A canonical transformation to collective variables for two particles is found, this satisfying the conditions of covarianee and the correct nonrelativistic limit. The action satisfies $n$ Hamilton–Jacobi equations. The scattering of two particles is considered. The nonuniqueness of the worldlines of the particles in the interaction region is discussed. 
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N. P. Klepikov; A. N. Shatnii. Formulation of the relativistic mechanics of systems of interacting particles. Teoretičeskaâ i matematičeskaâ fizika, Tome 46 (1981) no. 1, pp. 50-63. http://geodesic.mathdoc.fr/item/TMF_1981_46_1_a4/

[1] F. Rohrlich, Ann. Phys., 117 (1979), 292 | DOI | MR

[2] A. Komar, Gen. Rel. Grav., 7 (1976), 13 ; Phys. Rev., D18, 1881 ; 1887; (1978), 3617 | DOI | MR | Zbl | MR

[3] N. P. Klepikov, A. N. Shatnii, YaF, 31 (1980), 841 | MR

[4] L. P. Horwitz, C. Piron, Helv. Phys. Acta, 46 (1973), 316

[5] A. J. Macfarlane, Rev. Mod. Phys., 34 (1962), 41 | DOI | MR | Zbl

[6] D. D. Dionysiou, D. A. Vaiopoulos, Let. Nuovo Cim., 26 (1979), 5 | DOI

[7] O. B. Firsov, ZhETF, 24 (1953), 279

[8] H. M. L. Pryce, Proc. Roy. Soc., 195A (1949), 62 | MR

[9] M. Pauri, G. M. Prosperi, J. Math. Phys., 17 (1976), 1468 | DOI | MR | Zbl

[10] S. N. Sokolov, Preprint IFVE 78-125, 1978

[11] D. G. Currie, T. F. Jordan, A. C. G. Sudarshan, Rev. Mod. Phys., 35 (1963), 350 | DOI | MR

[12] H. Sazdjian, Nucl. Phys., B161 (1979), 469 | DOI | MR

[13] R. Giachetti, E. Sorace, Let. Nuovo Cim., 26 (1979), 1 | DOI

[14] B. Bakamjian, L. H. Thomas, Phys. Rev., 92 (1953), 1300 | DOI | MR | Zbl

[15] P. A. M. Dirac, Canad. J. Math., 2 (1950), 129 | DOI | MR | Zbl