Twisted Covariance and Weyl Quantisation

TL;DR

This paper clarifies that the tensor structure of noncommutative spacetime relations remains fundamental even in twisted Lorentz covariance frameworks, and explores the reasoning behind the choice of the theta parameter.

Contribution

It demonstrates the persistence of tensorial commutation relations in twisted spacetime quantization and investigates the motivation for selecting the theta matrix.

Findings

Tensor nature of commutation relations is fundamental in twisted approaches.

The paper provides insights into the reasoning behind the theta parameter.

Clarifies misconceptions about suppressing tensor structures in noncommutative geometry.

Abstract

In this letter we wish to clarify in which sense the tensor nature of the commutation relations [x^mu,x^nu]=i theta ^{mu nu} underlying Minkowski spacetime quantisation cannot be suppressed even in the twisted approach to Lorentz covariance. We then address the vexata quaestio "why theta"?