On spacetime algebra and its relations with negative masses

TL;DR

This paper explores the complexified spacetime algebra's structure, revealing four matter types with positive/negative masses and charges, and their relation to Lorentz group components and the Dirac equation.

Contribution

It introduces a novel analysis of spacetime algebra's subsets, linking them to matter properties and Lorentz group components, and examines their influence on the Dirac equation.

Findings

Four matter types with positive and negative masses and charges identified.

The four parts of spacetime algebra correspond to four connected components of the Lorentz group.

Implications for understanding matter-antimatter and charge-mass relationships.

Abstract

We consider four subsets of the complexified spacetime algebra, namely the real even part, the real odd part, the imaginary even part and the imaginary odd part. This naturally leads to the four connected components of the Lorentz group, supplemented each time by an additional symmetry. We then examine how these four parts impact the Dirac equation and show that four types of matter arise with positive and negative masses as well as positive and negative charges.