Model Dirac and Dirac-Hestenes equations as covariantly equipped systems of equations

TL;DR

This paper introduces a new class of covariantly equipped first-order PDE systems invariant under coordinate transformations, demonstrating that Dirac and Dirac-Hestenes equations are specific instances within this class, especially in pseudoeuclidean spaces.

Contribution

It defines a novel class of covariantly equipped PDE systems and shows that Dirac and Dirac-Hestenes equations are members of this class, linking them to symmetric hyperbolic systems.

Findings

Covariantly equipped systems can be expressed as Friedrichs symmetric hyperbolic systems.

Dirac and Dirac-Hestenes equations are shown to belong to this new class.

The systems are invariant under (pseudo)orthogonal coordinate changes.

Abstract

We define a new class of partial differential equations of first order (complex covariantly equipped systems of equations), which are invariant with respect to (pseudo)orthogonal changes of cartesian coordinates of (pseudo)euclidian space. It is shown that for pseudoeuclidian spaces of signature (1,n-1) covariantly equipped systems of equation can be written in the form of Friedrichs symmetric hyperbolic systems of equations of first order. We prove that Dirac and Dirac-Hestenes model equations belong to the class of covariantly equipped systems of equations.