Fermions and noncommutative theories

By using a framework where the object of noncommutativity θ represents independent degrees of freedom, we study the symmetry properties of an extended x + θ space-time, given by the group P ’, which has the Poincaré group P as a subgroup. In this process we use the minimal canonical extension of the Doplicher, Fredenhagen and Roberts algebra. It is also proposed a generalized Dirac equation, where the fermionic field depends not only on the ordinary coordinates but on θ as well. The dynamical symmetry content of such fermionic theory is discussed, and we show that its action is invariant under P’.