Formulation of axion-electrodynamics with Dirac fields

We propose a straightforward generalization of axion-electrodynamics (AED) for the case in which a lepton Dirac field is present in the U(1)EM gauge-invariant Lagrangian of the closed system. In the associated differential equations of motion we find that variations in the axion field give rise to modifications in the electric current and in the divergence of the axial current. In light of this, we interpret some possible Dark Matter (DM) phenomena. In particular, we discuss on general grounds (i) AED and DM, and (ii) DM axions interacting with leptons in a nonlinear electrodynamics background. We briefly comment on the conceivable application of this model beyond the subject of DM axions realized in condensed-matter physics.