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

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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. 
@article{TMF_1991_86_2_a6,
     author = {L. S. Kuz'menkov},
     title = {Field form of dynamics and statistics of systems of particles with electromagnetic interaction},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {231--243},
     publisher = {mathdoc},
     volume = {86},
     number = {2},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_86_2_a6/}
}
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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/