Equations of Motion and Energy-Momentum 1-Forms for the Coupled Gravitational, Maxwell and Dirac Fields

Abstract

A theory where the gravitational, Maxwell and Dirac fields (mathematically represented as particular sections of a convenient Clifford bundle) are treated as fields in Faraday’s sense living in Minkowski spacetime is presented. In our theory we obtain a genuine energy-momentum tensor for the gravitational field and a genuine energy-momentum conservation law for the system of the interacting gravitational, Maxwell and Dirac fields. Moreover, the energy-momentum tensors of the Maxwell and Dirac fields are symmetric, and it is shown that the equations of motion for the gravitational potentials are equivalent to Einstein equation of General Relativity. Precisely, the Einstein equation in which the second member is the sum of the energy-momentum tensors of the Maxwell, Dirac and the interaction Maxwell–Dirac fields all defined in an effective Lorentzian spacetime whose use is eventually no more than a question of mathematical convenience.