Generalized boson algebra and its entangled bipartite coherent states

Starting with a given generalized boson algebra U〈q〉(h(1)) known as the bosonized version of the quantum super-Hopf Uq(osp(1|2)) algebra, we employ the Hopf duality arguments to provide the dually conjugate function algebra Fun〈q〉(H(1)). Both the Hopf algebras being finitely generated, we produce a closed form expression of the universal T matrix that caps the duality and generalizes the familiar exponential map relating a Lie algebra with its corresponding group. Subsequently, using an inverse Mellin transform approach, the coherent states of single-node systems subject to the U〈q〉(h(1)) symmetry are found to be complete with a positive-definite integration measure. Nonclassical coalgebraic structure of the U〈q〉(h(1)) algebra is found to generate naturally entangled coherent states in bipartite composite systems. PACS numbers: 02.20.Uw, 02.30.Gp, 03.65.Ud