A no-pure-boost uncertainty principle from spacetime noncommutativity

TL;DR

This paper investigates how spacetime noncommutativity affects boost and rotation symmetries, revealing a fundamental limitation on pure boosts due to noncommutative geometry.

Contribution

It introduces a novel description of Lorentz transformations in kappa-Minkowski spacetime, showing the impossibility of pure boosts in this noncommutative setting.

Findings

Pure boosts are incompatible with noncommutative spacetime structure.

Conserved charges associated with rotations and boosts are identified.

Transformation parameters do not commute with spacetime coordinates.

Abstract

We study boost and space-rotation transformations in kappa-Minkowski noncommutative spacetime, using the techniques that some of us had previously developed (hep-th/0607221) for a description of translations in kappa-Minkowski, which in particular led to the introduction of translation transformation parameters that do not commute with the spacetime coordinates. We find a similar description of boosts and space rotations, which allows us to identify some associated conserved charges, but the form of the commutators between transformation parameters and spacetime coordinates is incompatible with the possibility of a pure boost.