The complete metric study of effective Dirac algebra

TL;DR

This paper provides a comprehensive metric analysis of the effective Dirac algebra in the context of relativistic hydrogen, revealing how electromagnetic interactions induce spacetime curvature, independent of algebraic representation.

Contribution

It offers the complete metric study of the effective Dirac algebra in both Dirac and Weyl presentations, demonstrating electromagnetic effects on spacetime curvature.

Findings

Electromagnetic interactions cause corrections to the flat spacetime metric.

The curved metric decomposes into a correction term and a projection tensor.

The curved metric is independent of the algebraic representation used.

Abstract

Following our work from the previous paper about the study of effective Dirac algebra and the metric of the simple, special case of relativistic hydrogen atom, this paper gives the complete metric study defined by the effective Dirac algebra in the Dirac and Weyl presentation, showing that relativistic electromagnetic interaction gives the correction of the flat background metric $\eta_{\mu\nu}$, thus curving spacetime. The curved metric can be nicely broken down into two parts, the pure correction on the flat spacetime metric and the projection tensor. We find that the curved metric is independent of the representation chosen.