Noncommutative Spherically Symmetric Space

We examine some noncommutative spherically symmetric spaces in three space dimensions. A generalization of Snyder’s noncommutative (Euclidean) space allows the inclusion of the generator of dilations into the defining algebra of the coordinate and rotation operators. We then construct a spherically symmetric noncommutative Laplacian on this space having the correct limiting spectrum. This is presented via a creation and annihilation operator realization of the algebra, which may lend itself to a truncation of the Hilbert space.