The spinor field theory of the photon

TL;DR

This paper proposes a novel spinor field theory for photons, unifying electromagnetic components into a spinor framework, leading to covariant quantization without vacuum divergence and a new positive frequency condition.

Contribution

It introduces a spinor formulation of the photon field, deriving a corresponding equation, and achieves covariant quantization that excludes vacuum divergence.

Findings

Photon field described as a spinor field

Covariant quantization without vacuum energy divergence

Introduction of a positive frequency condition

Abstract

I introduce a spinor field theory for the photon. The three-dimensional vector electromagnetic field and the four-dimensional vector potential are components of this spinor photon field. A spinor equation for the photon field is derived from Maxwell's equations,the relations between the electromagnetic field and the four-dimensional vector potential, and the Lorentz gauge condition. The covariant quantization of free photon field is done, and only transverse photons are obtained. The vacuum energy divergence does not occur in this theory. A covariant "positive frequency" condition is introduced for separating the photon field from its complex conjugate in the presence of the electric current and charge.