  A classical field theory is proposed for the electric current and the
electromagnetic field interpolating between microscopic and macroscopic
domains. It represents a generalization of the density functional for the
dynamics of the current and the electromagnetic field in the quantum side of
the crossover and reproduces standard classical electrodynamics on the other
side. The effective action derived in the closed time path formalism and the
equations of motion follow from the variational principle. The polarization of
the Dirac-see can be taken into account in the quadratic approximation of the
action by the introduction of the deplacement field strengths as in
conventional classical electrodynamics. Decoherence appears naturally as a
simple one-loop effect in this formalism. It is argued that the radiation time
arrow is generated from the quantum boundary conditions in time by decoherence
at the quantum-classical crossover and the Abraham-Lorentz force arises from
the accelerating charge or from other charges in the macroscopic or the
microscopic side, respectively. The functional form of quantum renormalization
group, the generalization of the renormalization group method for the density
matrix, is proposed to follow the scale dependence through the
quantum-classical crossover in a systematical manner.
