Noncommutative Spherically Symmetric Spaces

Abstract

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.

arXiv comment9 pages, revtex, matches Phys.Rev.D version

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Cited by in corpus (2)

• Hydrogen atom in rotationally invariant noncommutative space
• On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space