Field theory reformulated without self-energy parts: Divergence-free classical electrodynamics

This paper provides a formalism that allows the use of methods of statistical physics [R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics Wiley-Interscience, New York, 1975] 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 an infinite cutoff can be taken in an harmless way on self consistent equations. It combines without difficulties a manifestly gauge-invariant hamiltonian formulation of classical electrodynamics [R. Balescu, M. Poulain, Physica 76 (3) (1974) 421-444] with the reformulation of field theory without self-energy parts [M. de Haan, Ann. Phys. 311 (2004) 314-349]: all processes associated with self-energy are now integrated in a kinetic operator, while keeping the equivalence with the original description. 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.