Relativistic Kinetic Equations Including Radiation Effects. I. Vlasov Approximation

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Abstract
In a preceding series of papers, we developed relativistic statistical mechanics of electromagnetically interacting particles. Here we derive a hierarchy of manifestly covariant equations for the reduced densities. This hierarchy is valid at order one in a parameter which is closely related to radiation phenomena. At the lowest order (absence of correlation between particles), we derive a kinetic equation which is a modification of the relativistic Vlasov equation. The added term introduces the effects of the emission of collective radiation. A dimensional analysis shows that this term is important when mc 2 ∼ kT, i.e., when the plasma is relativistic. The modified Vlasov equation is shown to be irreversible: an H theorem is proved. Several applications are studied: dispersion relations, hydrodynamical equations. We have also discussed the Einstein‐Ritz controversy on the connection between retarded actions and irreversibility.

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