Photon quantum mechanics in real Hilbert space

TL;DR

This paper demonstrates that real electromagnetic fields used classically can be given a quantum interpretation with positive definite photon probability densities and standard observable operators, offering a covariant alternative to traditional quantum optics formulations.

Contribution

It introduces a quantum framework for real classical electromagnetic fields, establishing positive photon probability densities and covariant formulations, which differ from conventional complex field approaches.

Findings

Real fields have a quantum interpretation with positive photon probability density.

Operators for all standard physical observables are constructed within this framework.

A covariant alternative to the _{k}^{1/2} dependence in quantum optics is developed.

Abstract

Classically, electromagnetic pulses are described by real fields that couple to charged matter and propagate causally. We will show here that real fields of the form used in standard classical electromagnetic theory have a quantum mechanical interpretation in which the probability density for a photon to be at x is positive definite and operators representing all of the standard physical observables exist. A covariant alternative to the {\omega}_{k}^{1/2} dependence that appears in most (but not all) presentations of quantum optics and quantum field theory is presented and real scalar one photon advanced and retarded potentials are derived.