The (1,0)+(0,1) spinor description of the photon field and its preliminary applications

TL;DR

This paper develops a spinor-based formalism for the photon field using the (1,0)+(0,1) representation, enabling new insights into photon quantum theory, angular momentum, and gravitational interactions.

Contribution

It introduces a systematic spinor description of the electromagnetic field, facilitating analysis of photon properties and interactions in various contexts.

Findings

Provides a spinor formalism for the photon field.

Enables analysis of photon angular momentum and spin-orbit interaction.

Allows treatment of photon fields in curved spacetime with spin connection.

Abstract

Because spatio-temporal tensors are associated with the Lorentz group, whereas spinors are associated with its covering group SL(2, C), one can associate with every tensor a spinor (but not vice versa). In particular, the (1,0)+(0,1) representation of SL(2, C) can provide a six-component spinor equivalent to the electromagnetic field tensor. The chief aim of this work is to develop the (1,0)+(0,1) description for the electromagnetic field in the absence of sources, rigorously and systematically, which should be useful if we are to deal with those issues involving with single-photon states and the angular momentum of light, etc. Based on our formalism, the quantum theory and some symmetries of the photon field can be discussed in a new manner, and the spin-orbit interaction of photons can be described in a form that is closely analogous to that of the Dirac electron. Moreover, in terms of the (1,0)+(0,1) description, one can treat the photon field in curved spacetime via spin connection and the tetrad formalism, which is of great advantage to study the gravitational spin-orbit coupling of photons.