The Hyperbolic Clifford Algebra of Multivecfors

TL;DR

This paper explores the hyperbolic Clifford algebra of multivecfors, providing geometric interpretations, automorphisms, and algebraic properties relevant to hyperbolic spaces and spinor representations.

Contribution

It offers a detailed exposition of hyperbolic Clifford algebra, including geometric insights, automorphisms, and the algebraic structure of spinor-related ideals.

Findings

Introduction of Poincare automorphism (Hodge dual)

Geometric interpretation of vecfors and multivecfors

Analysis of algebraic properties of spinor-representing ideals

Abstract

In this paper we give a thoughtful exposition of the hyperbolic Clifford algebra of multivecfors which is naturally associated with a hyperbolic space, whose elements are called vecfors. Geometrical interpretation of vecfors and multivecfors are given. Poincare automorphism (Hodge dual operator) is introduced and several useful formulas derived. The role of a particular ideal in the hyperbolic Clifford algebra whose elements are representatives of spinors and resume the algebraic properties of Witten superfields is discussed.