Clifford Algebra of Two-Forms, Conformal Structures and Field Equations

TL;DR

This paper explores the relationship between duality operators on two-forms and conformal structures in four dimensions using Clifford algebra, and introduces new variants of Einstein's equations with potential physical implications.

Contribution

It provides a Clifford algebra framework linking duality and conformal structures, and proposes novel 'neighbours' of Einstein's equations with discussion on reality conditions.

Findings

Duality operators correspond to conformal structures in four dimensions.

Introduces new variants of Einstein's equations ('neighbours').

Discusses potential reality conditions for these variants.

Abstract

I review the equivalence between duality operators on two-forms and conformal structures in four dimensions, from a Clifford algebra point of view (due to Urbantke and Harnett). I also review an application, which leads to a set of "neighbours" of Einstein's equations. An attempt to formulate reality conditions for the "neighbours" is discussed.