Representations of Clifford algebras with hyperbolic numbers

TL;DR

This paper explores how hyperbolic numbers can be used to represent Clifford algebras, addressing discrepancies with conventional physics representations and providing illustrative examples.

Contribution

It introduces hyperbolic numbers as a tool to improve the representation of Clifford algebras in physics.

Findings

Hyperbolic numbers can close gaps in Clifford algebra representations.

Examples demonstrate the effectiveness of hyperbolic numbers in this context.

Potential for better alignment with physical conventions.

Abstract

The representations of Clifford algebras and their involutions and anti-involutions are fully investigated since decades. However, these representations do sometimes not comply with usual conventions within physics. A few simple examples are presented, which point out that the hyperbolic numbers can close this gap.