Observations on spacetime symmetry and non-commutativity

TL;DR

This paper explores a non-commutative spacetime framework where both coordinates and momenta are non-commutative, introducing a modified Lorentz symmetry that smoothly transitions to the standard symmetry, and discusses the Poincaré algebra in this context.

Contribution

It proposes a non-commutative Lorentz symmetry with a smooth limit to the classical case and analyzes the associated Poincaré algebra.

Findings

Defined a non-commutative Lorentz symmetry with a smooth classical limit

Analyzed the Poincaré algebra in non-commutative spacetime

Established a consistent framework connecting non-commutative and standard symmetries

Abstract

We consider both the co-ordinates and momenta to be non-commutative and define a non-commutative version of Lorentz symmetry which has a smooth limit to the standard Lorentz symmetry. The Poincar\acute{e} algebra in this spacetime has also been discussed.