Geodesic
Field form of dynamics and statistics of systems of particles with electromagnetic interaction
Teoretičeskaâ i matematičeskaâ fizika, Tome 86 (1991) no. 2, pp. 231-243 
L. S. Kuz'menkov. Field form of dynamics and statistics of systems of particles with electromagnetic interaction. Teoretičeskaâ i matematičeskaâ fizika, Tome 86 (1991) no. 2, pp. 231-243. http://geodesic.mathdoc.fr/item/TMF_1991_86_2_a6/
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     author = {L. S. Kuz'menkov},
     title = {Field form of dynamics and statistics of systems of particles with electromagnetic interaction},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1991_86_2_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that the equations of the dynamics of $N$ interacting particles can be represented for any $N$ in the form of a BBGKY hierarchy and a Liouville equation. A similar representation has been obtained for systems of charged particles in their electromagnetic self-field. This has made it possible to use the BBGKY hierarchy as a method of obtaining statistical equations. Transition to nondeterministic states of a particle-field system has the consequence that both the particle and the field states become nondeterministic due to the appearance of transition probabilities. The BBGKY hierarchy of evolution equations branches. In $7N$-dimensional phase spaces, there is no branching.

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