A Superspace Dirac Operator in NCG and the "factorization" of the Ordinary Dirac Operator

TL;DR

This paper reviews a method to factorize the Dirac operator using superspace techniques, aiming to bridge non-commutative geometry and supersymmetry, with applications to Euclidean and almost-commutative spaces.

Contribution

It introduces a formalism for factorizing the Dirac operator in superspace, connecting non-commutative geometry with supersymmetry frameworks.

Findings

Successful factorization of Minkowski space Dirac operator in superspace

Extension of the formalism to Euclidean space

Application to almost-commutative Dirac operators

Abstract

We review a procedure of factorizing the Minkowski space Dirac operator over a~suitable superspace, discuss its Euclidean space version and apply the worked out formalism in the case od an almost-commutative Dirac operator. The presented framework is an attempt to reconcile non-commutative geometry and supersymmetry.