Взаимодействие кватернионного поля Дирака с бозонным полем

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.