Action Of A Relativitic Charged Point Particle On Itself And Other Charges

The different expressions for the Green function of electromagneticrnfield of a point charge have been considered with the specialrnattention to the advanced contribution that is shown to be ofrnimportance for the self-action of particle responsible for thernradiation reaction. Simultaneous expansions for electromagnetic fieldsrnof a point charge are obtained in two different ways, by means ofrnLagrange expansions of the fields and the Taylor expansion of thernGreen function. The Lagrangian description for a system of chargedrnparticles and their electromagnetic field is given in terms ofrnparticle variables only, with the field expressed through the higherrnderivatives of the particles velocities. It is shown that thernself-actions of particles may be included in their equations of motionrnwith all divergent terms cancelled. An intrinisic relation between thernretarded and advanced fields of charged particles has been alsornobtained. The results are important for an exact description of arnsystem of relativistic charged particles

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