Quantised Calculus for Perturbed Massive Dirac Operator on Noncommutative Euclidean Space

Abstract

In this paper we study quantised calculus for the massive unperturbed Dirac operator \({\mathcal D}_{m}\), m > 0, as well as perturbed Dirac operator \({\mathcal D}_{m}+V\), on the noncommutative Euclidean space Open image in new window. We prove a necessary and sufficient condition Open image in new window for the quantised derivative \(i[\operatorname {sgn}({\mathcal D}_m+V), 1\otimes x]\) to belong to the weak Schatten ideal \({\mathcal L}_{d,\infty }\). This extends and generalises earlier results for Dirac operator on the classical Euclidean space.