Dynamical symmetries in noncommutative theories

TL;DR

This paper investigates how dynamical space-time symmetries operate in noncommutative relativistic theories using an extended space-time framework that includes noncommutativity parameters as independent degrees of freedom.

Contribution

It introduces a formalism that extends space-time to include noncommutativity variables and analyzes invariance under Poincaré and extended groups using Noether's theorem.

Findings

The formalism accommodates invariance under Poincaré and extended groups.

The extended space-time approach allows for a consistent treatment of noncommutative symmetries.

The Noether's formalism is successfully adapted to the extended space-time.

Abstract

In the present work we study dynamical space-time symmetries in noncommutative relativistic theories by using the minimal canonical extension of the Doplicher, Fredenhagen and Roberts algebra. Our formalism is constructed in an extended space-time with independent degrees of freedom associated with the object of noncommutativity $\theta^{\mu\nu}$. In this framework we consider theories that are invariant under the Poincar\'{e} group ${\cal P}$ or under its extension ${\cal P}'$, when translations in the extra dimensions are permitted. The Noether's formalism adapted to such extended $x+\theta$ space-time is employed.