  A manifestly gauge-invariant hamiltonian formulation of classical
electrodynamics has been shown to be relativistic invariant by the construction
of the adequate generators of the Poincare Lie algebra [Physica, 76, No. 3,
421-444 (1974)]. The original formulation in terms of reduced distribution
functions for the particles and the fields is applied here to the case of two
charges interacting through a classical electrodynamical field. On the other
hand, we have been able in previous work to introduce irreversibility at the
fundamental level of description [Ann. Phys., 311, 314-349 (2004)] by
reformulating field theory without self-energy parts by integrating all
processes associated with self-energy in a kinetic operator, while keeping the
equivalence with the original description [Prog. Theor. Phys.,109, 881-909
(2003)]. In this paper, the two approaches are combined to provide a formalism
that enables the use of methods of statistical physics to tackle the problem of
the divergence of the self-mass. Our approach leads to expressions that are
finite even for point-like charged particles: the limit of a infinite cutoff
can be taken in an harmless way on self consistent equations. In order to check
our theory, we recover the power dissipated by radiation in geometries where
the usual mass divergence does not play a role
