State-Vector Space and Canonical Coherent States in NoncommutativePlane

Abstract

The structure of the state-vector space of identical bosons innoncommutative spaces is investigated. To maintain Bose–Einsteinstatistics the commutation relations of phase space variablesshould simultaneously include coordinate-coordinatenon-commutativity and momentum-momentum non-commutativity, whichleads to a kind of deformed Heisenberg-Weyl algebra. Although thereis no ordinary number representation in this state-vector space,several set of orthogonal and complete state-vectors can bederived which are common eigenvectors of corresponding pairs ofcommuting Hermitian operators. As a simple application of thisstate-vector space, an explicit form of two-dimensional canonicalcoherent state is constructed and its properties are discussed.