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

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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. 
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     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},
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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/