Quantum-classical crossover in electrodynamics

TL;DR

This paper develops a classical field theory framework that smoothly transitions between quantum and classical electrodynamics, incorporating decoherence and radiation effects, and introduces a quantum renormalization group approach for scale dependence.

Contribution

It generalizes the density functional approach to include quantum-classical crossover in electrodynamics and introduces a quantum renormalization group method for systematic scale analysis.

Findings

Decoherence emerges naturally as a one-loop effect.

The radiation time arrow is generated from quantum boundary conditions.

The Abraham-Lorentz force is derived from charge acceleration.

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.