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

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 $A_{b}, \tilde{A}_{b}$.