The Photon Wavefunction: a covariant formulation and equivalence with QED

TL;DR

This paper develops a covariant Dirac-like equation for the photon wavefunction, demonstrating its equivalence with QED and clarifying its limitations in describing interacting photons.

Contribution

It introduces a covariant photon wavefunction formalism and shows its consistency with standard QED, highlighting its applicability mainly for free photons.

Findings

The photon wavefunction formalism reproduces classical electrodynamics with charged matter.

It is inconsistent for describing interacting photons in quantum theory.

The formalism simplifies the description of free photon propagation.

Abstract

We discuss the limits of the photon wavefunction (PWF) formalism, which is experiencing a revival in these days from the new practical applications in photonics and quantum optics. We build a Dirac-like equation for the PWF written in a manifestly covariant form and show that, in presence of charged matter fields, it reproduces the standard formulation of (classical) Electrodinamics. This shows the inconsistency of the attempts to construct a quantum theory of interacting photons, based on the so called photon wavefunction approach, alternative to standard QED. PWF formalism can then be used to provide an easier description of the propagation of free photons, when the photon number remains fixed in time.