Unification of versions of photon quantum mechanics through Clifford spacetime algebra

TL;DR

This paper reviews the Clifford spacetime algebra approach to Maxwell's equations, unifying various photon quantum mechanics formulations and deriving wave equations and conserved currents consistent with previous momentum space methods.

Contribution

It introduces a unified Clifford algebra framework that connects different photon quantum mechanics versions and derives consistent wave equations and conserved quantities.

Findings

Derived photon wave equations from Clifford algebra

Established a conserved four-current in the algebraic framework

Showed agreement with previous momentum space formulations

Abstract

The Clifford spacetime algebraic description of Maxwell's equations is reviewed and shown to give a unified picture of recently published versions of photon quantum mechanics. Photon wave equations and a conserved four-current are derived from the complexified standard Lagrangian. The equations of motion and scalar product are found to be in good agreement with those obtained from Fourier transformation of momentum space wave function and scalar product [Phys. Rev. A 102, 042201 (2020)].