Quantum Mechanics on a Noncommutative Brane in M ( atrix ) Theory

Abstract

We consider the quantum mechanics of a particle on a noncommutative two-sphere with the coordinates obeying an SU(2)-algebra. The momentum operator can be constructed in terms of an SU(2) × SU(2)-extension and the Heisenberg algebra recovered in the smooth manifold limit. Similar considerations apply to the more general SU(n) case. 

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