**Author details**

4.Solutions of the new Dirac spacetime matrix equation can be easily

using the linear transformation matrix *Z*.

current densities.

equation.

*Progress in Relativity*

**Acknowledgements**

sectors.

**36**

transformed into solutions satisfying the traditional relativistic Dirac equation

5. The Dirac spacetime matrix equation is equivalent to four new relativistic quantum mechanical vector equations. We referred to these equations as the Dirac spacetime vector equations. In the absence of electromagnetic potentials, these vector equations resemble the four classical electromagnetic microscopic Maxwell field vector equations in the absence of charge and

6.Multiplication of the Dirac spacetime matrix equation by the spacetime matrix operator *M*^ leads to the relativistic Klein-Gordon spacetime matrix

eigenvectors satisfying the traditional Dirac equation.

obtained may suggest new physics.

7. Four transverse orthonormal eigenvectors as well as the four non-transverse orthonormal eigenvectors satisfying the Dirac spacetime matrix equation map, via the linear transformation matrix *Z*, into the same set of four orthonormal

8. A new generalized spacetime matrix equation employing the operator *M*^ was introduced. This equation is a generalization of the Maxwell and Dirac

spacetime matrix equations for free space. We explored time-harmonic planewave solutions of this equation as well as their properties. Some of results

We are most appreciative of the help by Ms. Trin Riojas of the Optical Sciences Center in coordinating computer station inputs/outputs between authors and publishers. The past informal discussions with Dr. Arvind S. Marathay of the Optical Sciences Center are also greatly appreciated. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit

> Richard P. Bocker<sup>1</sup> \* † and B. Roy Frieden2†

1 San Diego State University, San Diego, California, United States of America


† These authors contributed equally.

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
