Dirac-K\"{a}hler field, spinor technique, and 2-potential approach to electrodynamics with two charges

TL;DR

This paper derives spinor and tensor equations for two types of massless photon fields with different parities, showing how their combination reproduces Maxwell's electrodynamics with electric and magnetic charges, and extends the theory to curved spacetime.

Contribution

It introduces a novel two-potential approach for electrodynamics with two photon types of different parities, including magnetic charges, and extends the duality transformation to curved spacetime.

Findings

Derived spinor equations for two photon types with different parities.

Showed that combining these fields yields Maxwell electrodynamics with magnetic charges.

Extended the theory and duality transformation to curved spacetime.

Abstract

From the 16-component Dirac-K\"{a}hler field theory, spinor equations for two types of massless vector photon fields with different parities have been derived. Their equivalent tensor equations in terms of the strength tensor $F_{ab}$ and respective 4-vector $A_{b}$ and 4-pseudovector $\tilde{A}_{b}$ depending on intrinsic photon parity are derived; they include additional sources, electric 4-vector $j_{b}$ and magnetic 4-pseudovector $\tilde{j}_{b}$. The theories of two types of photon fields are explicitly uncoupled, their linear combination through summing or subtracting results in Maxwell electrodynamics with electric and magnetic charges in 2-potential approach. So the problem of existence of magnetic charge can be understood as a super selection rule for different photon fields in intrinsic parity. The whole analysis is extended straightforwardly to a curved space-time background. In the frames of that extended Maxwell theory, the known electromagnetic duality is described as a linear transformation mixing the field variables referred to photons with different parities. That extended dual transformation concerns both strength tensors and 4-potentials $A_{b}, \tilde{A}_{b}$.