The quantum electromagnetic field in the Weyl-Wigner representation

TL;DR

This paper reformulates the quantum electromagnetic field using the Weyl-Wigner representation, providing a framework that aligns quantum and classical descriptions and offers a local realistic interpretation of Bell test experiments.

Contribution

It introduces a Weyl-Wigner formalism for the quantum EM field, enabling classical-like interpretation and analysis of quantum experiments within a unified phase-space approach.

Findings

The formalism is equivalent to the standard Hilbert space approach.

It allows interpretation of experiments with classical-like fields.

A local realistic interpretation of a Bell inequality test is proposed.

Abstract

The quantum electromagnetic (EM) field is formulated in the Weyl-Wigner representation (WW), which is equivalent to the standard Hilbert space one (HS). In principle it is possible to interpret within WW all experiments involving the EM field interacting with macroscopic bodies, the latter treated classically. In the WW formalism the essential difference between classical electrodynamics and the quantum theory of the EM field is\ just the assumption that there is a random EM field filling space\QTR{it}{, }i.e. the existence of a zero-point field with a Gaussian distribution for the field amplitudes. I analyze a typical optical test of a Bell inequality. The model admits an interpretation compatible with local realism, modulo a number of assumptions assumed plausible.