Title: Matter fields interacting with photons,
Abstract: We have extended the biquaternionic Dirac's equation to include interactions
with photons. The electric field is found to be perpendicular to the matter
magnetic field, and the magnetic field is perpendicular to the matter inertial
field. Inertial and magnetic masses are found to be conserved separately. The
magnetic mass density is a consequence of the coupling between the vector
potential and the matter inertial field. The presence of the vector and scalar
potentials, and the matter inertial and magnetic fields are found to modify the
standard form of the derived Maxwell's equations. The resulting interacting
electrodynamics equations are found to generalize those of axion-like fields of
Frank Wilczek or Chern-Simons equations. The axion field satisfies massive
Klein-Gordon equation if Lorenz gauge condition is violated. Therefore, axion
could be our massive photon. The electromagnetic field vector,
$\vec{F}=\vec{E}+ic\vec{B}$, is found to satisfy massive Dirac's equation in
addition to the fact that $\vec{\nabla}\cdot\vec{F}=0$, where $\vec{E}$ and
$\vec{B}$ are the electric and magnetic fields, respectively.