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

Abstract

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. Copyright © 2014 John Wiley & Sons, Ltd.