Lorentz Covariant k-Minkowski Spacetime

TL;DR

This paper constructs a covariant formulation of k-Minkowski spacetime, clarifying its relation to deformed Lorentz symmetry and discussing implications for noncommutative geometry.

Contribution

It introduces a minimal canonical covariantisation of k-Minkowski spacetime and compares it to deformed Lorentz covariance, providing new insights into noncommutative spacetime frameworks.

Findings

Covariantisation of k-Minkowski spacetime is achieved.

Deformed Lorentz covariance is equivalent to a non covariant restriction.

The framework clarifies the interpretation of Lorentz covariance in noncommutative geometry.

Abstract

In recent years, different views on the interpretation of Lorentz covariance of non commuting coordinates were discussed. Here, by a general procedure, we construct the minimal canonical central covariantisation of the k-Minkowski spacetime. We then show that, though the usual k-Minkowski spacetime is covariant under deformed (or twisted) Lorentz action, the resulting framework is equivalent to taking a non covariant restriction of the covariantised model. We conclude with some general comments on the approach of deformed covariance.