On a connection between the Maxwell system, the extended Maxwell system, the Dirac operator and gravito-electromagnetism

The close connection between Maxwell's equations and the Dirac equation is under consideration in a rigorous functional analytical framework. The two systems are linked via the so-called extended Maxwell system Picard R. A structural observation for linear material laws in classical mathematical physics. Mathematical Methods in the Applied Sciences 2009;32(14):1768–1803, which is here re-considered in the time-dependent case as an evolutionary space-time operator equation. This structural observation is then applied to recover and generalize the equations of gravito-electromagnetism and to reformulate theMaxwell-Dirac system as a system of three coupled extended Maxwell systems. This reformulation rests on the observation that what in electrodynamics is commonly known as 'potential' is actually a solution to another extended Maxwell system.