State-Vector Space and Canonical Coherent States in Noncommutative Plane
Sicong Jing, Tao Ling-Ping, Qiuyu Liu +1 more
The structure of the state-vector space of identical bosons in noncommutative spaces is investigated. To maintain Bose–Einstein statistics the commutation relations of phase space variables should simultaneously include coordinate-coordinate non-commutativity and momentum-momentum non-commutativity, which leads to a kind of deformed Heisenberg-Weyl algebra. Although there is no ordinary number representation in this state-vector space, several set of orthogonal and complete state-vectors can be derived which are common eigenvectors of corresponding pairs of commuting Hermitian operators. As a simple application of this state-vector space, an explicit form of two-dimensional canonical coherent state is constructed and its properties are discussed.
arXiv:hep-th/0505048•Communications in Theoretical Physics•Feb 1, 2006•6 citations