Field Theory reformulated without self - energy parts . Classical electrodynamics

A manifestly gauge-invariant hamiltonian formulation [1] of classical electrodynamics has been shown to be relativistic invariant by the construction of the generators of the Poincare Lie algebra. The original formulation in terms of reduced distribution functions for the particles is applied here to the case of two charges interacting through the classical electrodynamical field. A reduced description is also introduced for describing the electric and magnetic transverse components of the field. In our quest towards the introduction of irreversibility at the fundamental level of description [2], we have introduced a reformulation of field theory without self-energy parts that enables to take properly into account all processes associated with self-energy in a kinetic operator, while keeping the equivalence with the original description. When the acceleration vector is perpendicular to the velocity vector, the usual mass divergence does not play a role for the computation of the dissipated power. A divergence-free expression can be obtained in these circonstances and avoids the problem of runaway solutions since, in the present formalism, it is expressed in terms of the time derivative of the mean force and not the time derivative of the acceleration as provided by the usual approach.