Localizability in $\kappa$-Minkowski Spacetime

TL;DR

This paper explores the structure of $$-Minkowski spacetime using quantum mechanics, highlighting the use of Mellin transforms as an analogue to Fourier transforms and discussing observer roles.

Contribution

It introduces a novel approach to analyze $$-Minkowski space with quantum operators and extends previous work by incorporating Mellin transforms.

Findings

Mellin transforms serve as the analogue of Fourier transforms in this context

The study clarifies the role of transformations and observers in noncommutative spacetime

Provides a framework for understanding quantum spacetime using standard quantum mechanics

Abstract

Using the methods of ordinary quantum mechanics we study $\kappa$-Minkowski space as a quantum space described by noncommuting self-adjoint operators, following and enlarging arXiv:1811.08409. We see how the role of Fourier transforms is played in this case by Mellin transforms. We briefly discuss the role of transformations and observers.