The Mean-Field Limit for a Regularized Vlasov-Maxwell Dynamics

The present work establishes the mean-field limit of a N-particle system towards a regularized variant of the relativistic Vlasov-Maxwell system, following the work of Braun-Hepp [Commun Math Phys 56:101-113, 1977] and Dobrushin [Func Anal Appl 13:115-123, 1979] for the Vlasov-Poisson system. The main ingredients in the analysis of this system are (a) a kinetic formulation of the Maxwell equations in terms of a distribution of electromagnetic potential in the momentum variable, (b) a regularization procedure for which an analogue of the total energy-i. e. the kinetic energy of the particles plus the energy of the electromagnetic field-is conserved and (c) an analogue of Dobrushin's stability estimate for the Monge-Kantorovich-Rubinstein distance between two solutions of the regularized Vlasov-Poisson dynamics adapted to retarded potentials.