Quantum-classical crossover in electrodynamics

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.

new references added, few sign errors fixed, to appear in Physical Review D

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• Dynamical breakdown of time reversal invariance and causality
• Scattering in an environment
• Sub-classical fields and polarization in electrodynamics
• The Abraham-Lorentz force and electrodynamics at the classical electron radius
• Semiclassical Coulomb field
• Renormalization-Group Running Induced Cosmic Inflation
• A nonequilibrium renormalization group approach to turbulent reheating
• Radiation reaction from quantum electrodynamics and its implications for the Unruh effect
• Environment Induced Time Arrow and the Closed Time Path method
• Decoherence and damping in ideal gases
• Renormalization of the bilocal sine-Gordon model
• Spontaneous breakdown of the time reversal symmetry