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.

9 pages, revtex, matches Phys.Rev.D version

References in corpus (5)

• Spectrum of the non-commutative spherical well
• Spherically Symmetric Noncommutative Space: d = 4
• A universal Dirac operator and noncommutative spin bundles over fuzzy complex projective spaces
• Fuzzy Riemann Surfaces
• Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives

Cited by in corpus (1)

• Hydrogen atom in rotationally invariant noncommutative space