$\kappa$-Minkowski and Snyder algebra from reparametrisation symmetry

TL;DR

This paper derives combined $$-Minkowski and Snyder noncommutative phase-space structures using reparametrisation symmetry of a point particle Lagrangian consistent with Doubly Special Relativity.

Contribution

It introduces a novel approach to obtain combined noncommutative phase-space structures from reparametrisation symmetry in DSR frameworks.

Findings

Derived noncommuting phase-space structures combining $$-Minkowski and Snyder algebra.

Utilized reparametrisation symmetry of a DSR-compatible point particle Lagrangian.

Extended the understanding of noncommutative geometries in relativistic particle models.

Abstract

Following our earlier work \cite{sunandan1, sunandan2}, we derive noncommuting phase-space structures which are combinations of both the $\kappa$-Minkowski and Snyder algebra by exploiting the reparametrisation symmetry of the recently proposed Lagrangian for a point particle \cite{subir} satisfying the exact Doubly Special Relativity dispersion relation in the Magueijo-Smolin framework.