Extended pseudo-fermions from non commutative bosons

Abstract

We consider some modifications of the two dimensional canonical commutation relations, leading to non commutative bosons and we show how biorthogonal bases of the Hilbert space of the system can be obtained out of them. Our construction extends those recently introduced by one of us (FB), modifying the canonical anticommutation relations. We also briefly discuss how bicoherent states, producing a resolution of the identity, can be defined.