Metric and Gauge Extensors

TL;DR

This paper develops tools for multivector calculus in differential geometry, introducing metric and gauge extensors, and presents a formula that simplifies calculations in Clifford algebras by relating them to Euclidean cases.

Contribution

It introduces metric and gauge extensors, pseudo-orthogonal metric extensors, and the golden formula, enabling easier computation in Clifford algebras related to differential geometry.

Findings

Introduction of metric and gauge extensors

Proof of the golden formula for Clifford algebras

Cl(V,G) as a deformation of Cl(V,G_E)

Abstract

In this paper, the second in a series of eight we continue our development of the basic tools of the multivector and extensor calculus which are used in our formulation of the differential geometry of smooth manifolds of arbitrary topology . We introduce metric and gauge extensors, pseudo-orthogonal metric extensors, gauge bases, tetrad bases and prove the remarkable golden formula, which permit us to view any Clifford algebra Cl(V,G) as a deformation of the euclidean Clifford algebra Cl(V,G_{E}) discussed in the first paper of the series and to easily perform calculations in Cl(V,G) using Cl(V,G_{E}).