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 TMF, 1991, Volume 86, Number 2, Pages 231–243 (Mi tmf5438)

Field form of dynamics and statistics of systems of particles with electromagnetic interaction

L. S. Kuz'menkov

Abstract: 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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English version:
Theoretical and Mathematical Physics, 1991, 86:2, 159–168

Bibliographic databases:

Citation: L. S. Kuz'menkov, “Field form of dynamics and statistics of systems of particles with electromagnetic interaction”, TMF, 86:2 (1991), 231–243; Theoret. and Math. Phys., 86:2 (1991), 159–168

Citation in format AMSBIB
\Bibitem{Kuz91} \by L.~S.~Kuz'menkov \paper Field form of dynamics and statistics of systems of particles with electromagnetic interaction \jour TMF \yr 1991 \vol 86 \issue 2 \pages 231--243 \mathnet{http://mi.mathnet.ru/tmf5438} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1107704} \transl \jour Theoret. and Math. Phys. \yr 1991 \vol 86 \issue 2 \pages 159--168 \crossref{https://doi.org/10.1007/BF01016167} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991GH61300007} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. A. Drofa, L. S. Kuz'menkov, “Continual approach to the multiparticle systems with long-range interaction. Hierarchy of macroscopic fields and some physical consequences”, Theoret. and Math. Phys., 108:1 (1996), 849–859
2. I. M. Aleshin, “Magnetohydrodynamics with regard to electron inertia: Some exact solutions”, Theoret. and Math. Phys., 116:3 (1998), 1011–1020
3. L. S. Kuz'menkov, S. G. Maksimov, “Quantum hydrodynamics of particle systems with Coulomb interaction and quantum Bohm potential”, Theoret. and Math. Phys., 118:2 (1999), 227–240
4. L. S. Kuz'menkov, S. G. Maksimov, “Distribution Functions in Quantum Mechanics and Wigner Functions”, Theoret. and Math. Phys., 131:2 (2002), 641–650
5. I. M. Aleshin, O. O. Trubachev, “Equilibrium State of Inhomogeneous Plasma”, Theoret. and Math. Phys., 138:1 (2004), 134–141
6. Ivanov A.Yu. Andreev P.A. Kuz'menkov L.S., “Balance Equations in Semi-Relativistic Quantum Hydrodynamics”, Int. J. Mod. Phys. B, 28:21 (2014), 1450132
7. Andreev P.A., “Quantum Kinetics of Spinning Neutral Particles: General Theory and Spin Wave Dispersion”, Physica A, 432 (2015), 108–126
8. Andreev P.A., “NLSE for quantum plasmas with the radiation damping”, Mod. Phys. Lett. B, 30:13 (2016), 1650180
9. Andreev P.A., “Radiative Corrections to the Coulomb Law and Model of Dense Quantum Plasmas: Dispersion of Longitudinal Waves in Magnetized Quantum Plasmas”, Phys. Plasmas, 25:4 (2018), 042103
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