Discretizing the deformation parameter in the suq(2) quantum algebra

Abstract

Inspired in recent works of Biedenharn [1, 2] on the realization of the q-algebra suq (2), we show in this note that the condition [2j + 1]q = Nq(j) = integer, implies the discretization of the deformation parameter α, where q = eα. This discretization replaces the continuum associated to α by an infinite sequence α1, α2, α3, ..., obtained for the values of j, which label the irreps of suq(2). The algebraic properties of Nq(j) are discussed in some detail, including its role as a trace, which conducts to the Clebsch-Gordan series for the direct product of irreps. The consequences of this process of discretization are discussed and its possible applications are pointed out. Although not a necessary one, the present prescription is valuable due to its algebraic simplicity especially in the regime of appreciable values of α.