Spectral Distance on Lorentzian Moyal Plane

TL;DR

This paper introduces an operatorial method using Hilbert-Schmidt operators to compute spectral distances in the Lorentzian Moyal plane, revealing no non-commutative deformations unlike in Euclidean cases.

Contribution

It provides a novel operatorial approach to spectral distances in Lorentzian non-commutative geometry, specifically for the Moyal plane, with new insights into non-commutative effects.

Findings

No non-commutative deformations observed in spectral distances

Operatorial approach effectively computes distances between time-like separated events

Results differ from Euclidean non-commutative geometries

Abstract

We present here a completely operatorial approach, using Hilbert-Schmidt operators, to compute spectral distances between time-like separated "events ", associated with the pure states of the algebra describing the Lorentzian Moyal plane, using the axiomatic framework given by [13, 14]. The result shows no deformations of non-commutative origin, as in the Euclidean case.