Quantum Mechanics on a Noncommutative Brane in M(atrix) Theory
V.P. Nair
TL;DR
This paper explores the quantum mechanics of particles on noncommutative spheres, extending to SU(n) cases, and shows how classical limits recover familiar algebraic structures.
Contribution
It introduces a framework for quantum mechanics on noncommutative spheres using SU(2) and SU(n) algebras, connecting noncommutative geometry with traditional quantum mechanics.
Findings
Constructed momentum operators using SU(2)×SU(2) extension
Recovered Heisenberg algebra in the smooth limit
Extended considerations to SU(n) cases
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 -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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