THE DISPERSION EQUATION FOR ELECTROMAGNETIC FIELD IN THE ENVIRONMENT

The eigenwaves of the electromagnetic field in a medium that contains charges are considered. The quasiparticle approach is implemented immediately. For this purpose the Hamiltonian of the field oscillators in medium is extracted from the general non-relativistic Hamiltonian. The remaining terms with the electromagnetic field operators in the Hamiltonian formed a small renormalized interaction of the electromagnetic field with a medium. The perturbation theory in the mentioned above interaction is built. A statistical operator of the system is found up to the first-order perturbation theory. To this end Bogolyubov's principle of correlation weakening and the thermodynamics perturbation theory are used. The operator Maxwell's equations are averaged with the statistical operator of the system. The averaged electric current is found. After that we obtain the homogeneous linear differential equation with coefficients that do not depend on time. Te dispersion equation of the electromagnetic field in the medium as the characteristic equation is received. A quasiparticle dispersion law is the solution of the characteristic equation based on the self-consistency. The classical electron plasma is considered as an example of the application of the obtained results. The standard dispersion laws for big and small phase velocities of electromagnetic processes in such plasma are obtained.