Remarks on Relativistic Statistical Mechanics. II. Hierarchies for the Reduced Densities

Abstract

In Paper I the basis of relativistic statistical mechanics was discussed and notions such as phase space, Gibbs ensemble, distribution functions were defined. Paper II deals with hierarchies of equations for the reduced densities. Extensive use is made of the beautiful methods of Klimontovich. In this way ``classical mesic interactions'' are dealt with neglecting ``radiation'' effects (i.e., ``classical'' emission of mesons). It is shown how the ``renormalization of mass'' affects the hierarchies obtained. Electromagnetic interactions are dealt with: (a) neglecting radiation effects, (b) including radiation effects. The latter case is treated on the basis of the Lorentz-Dirac equations and with the help of suitable modifications of the formalism. In this way a new approach to radiation phenomena (for instance, in plasmas) is obtained. Finally, as a matter of illustration, several well-known relativistic kinetic equations are rederived in a slightly improved manner (i.e., Vlasov and Landau equations).