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 $\theta^{\mu\nu}$. 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.