Axion-electrodynamics and the Poynting theorem

In a recent study, we proposed an axion-electrodynamics model that consistently incorporates a lepton Dirac field into the gauge-invariant Lagrangian of a closed physical system. Our investigation delved toward potential applications of the model, with a focus on its implications in the realm of Dark Matter axions interacting with leptons in a nonlinear electrodynamics background. In the present work, we introduce an extended axion-electrodynamics model wherein the Bianchi identities are modified by the axion field. This leads to a modification of the energy conservation law for the fields: the Poynting theorem in a source-free region, in which the axion field is involved. By implementing a quantization scheme, our model can offer a novel approach for addressing the problem of axion production/conversion in the presence of electromagnetic and Dirac fields.