Dynamical symmetries in noncommutative theories

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 ${\ensuremath{\theta}}^{\ensuremath{\mu}\ensuremath{\nu}}$. In this framework we consider theories that are invariant under the Poincar\'e group $\mathcal{P}$ or under its extension ${\mathcal{P}}^{\ensuremath{'}}$, when translations in the extra dimensions are permitted. The Noether's formalism adapted to such extended $x+\ensuremath{\theta}$ space-time is employed.