Spinors in the hyperbolic algebra

TL;DR

This paper introduces a novel algebraic approach to representing relativistic vectors and spinors using the three-dimensional universal complex Clifford algebra, avoiding explicit matrix representations.

Contribution

It develops an algebraic formulation of spinors in the hyperbolic algebra, extending the Hestenes spacetime approach without relying on matrices.

Findings

Algebraic representation of relativistic vectors as paravectors

Introduction of spinors in the hyperbolic algebra framework

Elimination of explicit matrix dependence in spinor representation

Abstract

The three-dimensional universal complex Clifford algebra is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the dependance on an explicit matrix representation of the algebra.