Spinor wave equation, relativistic condition, and nonlocality of photon spin

TL;DR

This paper derives the photon spin from quantum equations, revealing its nonlocal nature and how it transforms under Lorentz transformations, highlighting the intrinsic and nonlocal properties of photon spin.

Contribution

It reinterprets Darwin's equations for photon quantum mechanics, showing photon spin as a nonlocal, Lorentz-transforming spinor derived from a modified wave equation.

Findings

Photon wavefunction transforms as a spinor under Lorentz transformations.

Photon spin is intrinsic but nonlocal due to the constraint equation.

The wave equation predicts a form of photon spin as an intrinsic degree of freedom.

Abstract

The purpose of this paper is to derive the photon spin and to deduce its properties from a pair of quantum equations for the photon. To this end, Darwin's equations are reinterpreted so as to meet the need of the quantum mechanics of the photon. It is found that the photon wavefunction transforms under Lorentz transformation as a spinor. The relativistic nature of the photon is expressed through a constraint equation on the wavefunction in such a way that the wave equation, which takes on the form of the Schr\"{o}dinger equation, is not Lorentz covariant unless the constraint equation is taken into account. The wave equation predicts the existence of a kind of spin, an intrinsic degree of freedom. But the constraint equation makes the spin nonlocal in the sense that no unique local density exists for the spin in position space. The nonlocality of the photon spin is a reflection of the nonlocality of the photon itself.