Quantum-classical crossover in electrodynamics
Janos Polonyi
Abstract
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.