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

摘要

A theory where the gravitational, Maxwell and Dirac fields (mathematicallyrepresented as particular sections of a convenient Clifford bundle) aresupposed fields in Faraday's sense living in Minkowski spacetime is presented.In our theory there exist a genuine energy-momentum tensor for thegravitational field and a genuine energy-momentum conservation law for thesystem of the interacting gravitational, Maxwell and Dirac fields. Moreover,the energy-mometum tensors of the Maxwell and Dirac fields are symmetric, andit is shown that the equations of motion for the gravitational potentials isequivalent to Einstein equation of General Relativity (where the second memberis the sum of the energy-momentum tensors of the Maxwell, Dirac and interactionMaxwell-Dirac fields) defined in an effective Lorentzian spacetime, whose useis eventually no more than a question of mathematical convenience.