Known the Bohm-Pines Coulomb plasma theory reducing the system to subsystem of electrons with short range effective interaction and one for plasmons which interact each other has been generalized for general case of weak relativistic plasma and electromagnetic field. Problem of appearance in the theory of new grades of freedom was solved.

We investigate the kinetics of the electromagnetic field in a hydrodynamic medium containing charged particles. A closed system of equations of the electromagnetic field and hydrodynamic equations taking into account dissipative processes is constructed. To describe the electromagnetic field, we use its average values and the corresponding binary correlation functions as new independent variables. The reverse influence of the field on the medium is studied. The investigation is based on quasirelativistic quantum electrodynamics in the Hamilton gauge and on the Bogolyubov method of reduced description of nonequilibrium processes.

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Closed system of equations for binary correlations of electromagnetic field and hydrodynamic medium (many component plasma) has been obtained and linearized near equilibrium. Ideal gas approximation was studied. Coupled hydrodynamic and transversal plasma waves for correlations of electromagnetic field was predicted.