Quantum Distributions for the Electromagnetic Field

TL;DR

This paper explores the quantum distributions of the electromagnetic field, linking classical wave coherence to quantum phase-space distributions, and demonstrating the evolution towards thermal equilibrium using Wigner functions.

Contribution

It introduces a phase-space approach to quantum electromagnetic fields, connecting classical coherence with quantum distributions and analyzing their thermal evolution.

Findings

Wigner functions for photons evolve towards Planck distribution.

Electromagnetic fields can be described in states of definite helicity.

Classical wave coherence is related to quantum phase-space distributions.

Abstract

The coherence properties of the classical waves are discussed in terms of the Cauchy problem for the wave equation, and of a discrete representation by an ensemble of Hamiltonian systems. Wave quanta are related to specific "action fields", and phase-space distributions of phonons and photons are obtained by Wigner transform. For photons in a thermal environment, the proposed Wigner function evolves towards the Planck equilibrium distribution. It is shown that the free electromagnetic field can also be found in states of definite helicity, described by a complex vector potential.