Photon wave function and zitterbewegung

TL;DR

This paper develops a Lorentz-covariant Dirac-like formalism for the photon wave function, linking electric-magnetic duality to positive and negative energy solutions, and explores photon zitterbewegung arising from virtual photons.

Contribution

It introduces a unified Lorentz-covariant framework for photon fields and clarifies the nature of photon zitterbewegung related to virtual longitudinal and scalar photons.

Findings

Photon zitterbewegung occurs only with virtual longitudinal and scalar photons.

The formalism links electric-magnetic duality to energy solution duality.

Photon polarization vectors describe ZB motion vector properties.

Abstract

In terms of a photon wave function corresponding to the (1, 0)+(0, 1) representation of the Lorentz group, the radiation and Coulomb fields within a source-free region can be described unitedly by a Lorentz-covariant Dirac-like equation. In our formalism, the relation between the positive- and negative-energy solutions of the Dirac-like equation corresponds to the duality between the electric and magnetic fields, rather than to the usual particle-antiparticle symmetry. The zitterbewegung (ZB) of photons is studied via the momentum vector of the electromagnetic field, which shows that only in the presence of virtual longitudinal and scalar photons, the ZB motion of photons can occur, and its vector property is described by the polarization vectors of the electromagnetic field.