Extended pseudo-fermions from non commutative bosons

TL;DR

This paper explores modifications to two-dimensional canonical commutation relations resulting in non-commutative bosons, constructing biorthogonal bases and discussing bicoherent states with resolution of identity.

Contribution

It introduces a new framework for non-commutative bosons by extending previous models and constructs biorthogonal bases and bicoherent states within this setting.

Findings

Biorthogonal bases can be derived from modified commutation relations.

The construction extends previous models of non-commutative bosons.

Bicoherent states with resolution of the identity are discussed.

Abstract

We consider some modifications of the two dimensional canonical commutation relations, leading to {\em 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.