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

TL;DR

This paper develops a unified framework for gravitational, electromagnetic, and Dirac fields in Minkowski spacetime, establishing genuine energy-momentum tensors and conservation laws, and linking gravitational equations to Einstein's equations in an effective spacetime.

Contribution

It introduces a novel formulation with genuine energy-momentum tensors for all fields and connects gravitational equations to Einstein's equations within an effective Lorentzian spacetime.

Findings

Existence of genuine energy-momentum tensors for gravitational, Maxwell, and Dirac fields.

Proof of energy-momentum conservation laws for the coupled system.

Equivalence of gravitational equations to Einstein's equations in an effective spacetime.

Abstract

A theory where the gravitational, Maxwell and Dirac fields (mathematically represented as particular sections of a convenient Clifford bundle) are supposed fields in Faraday's sense living in Minkowski spacetime is presented. In our theory there exist 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-mometum tensors of the Maxwell and Dirac fields are symmetric, and it is shown that the equations of motion for the gravitational potentials is equivalent to Einstein equation of General Relativity (where the second member is the sum of the energy-momentum tensors of the Maxwell, Dirac and interaction Maxwell-Dirac fields) defined in an effective Lorentzian spacetime, whose use is eventually no more than a question of mathematical convenience.