Geodesic
Example of a one-time many-particle relativistic wave equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 18 (1974) no. 1, pp. 56-65 
S. N. Sokolov. Example of a one-time many-particle relativistic wave equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 18 (1974) no. 1, pp. 56-65. http://geodesic.mathdoc.fr/item/TMF_1974_18_1_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

An example is given of a relativistic wave equation of a system of $N$ particles with interaction potential containing only $N$-particle forces. The equation is formulated in the variables $t$, $g_1$, $g_2,\dots$, where $g_i$ are the three-dimensional parts of the four-velocities, and the equation is a direct generalization of the Sehrödinger equation in the $p$-representation. The transformations of the wave function allowed by the equation form a group that is isomorphic to the Poincare group and, when the interaction is switched off, they form a group that is isomorphic to the direct product of Poincare groups. An analog of the configuration $x$-space is constructed and it is shown that the equation is consistent with classical relativistic mechanics of many bodies.

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