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arXiv:hep-th/0609117 · Journal of High Energy Physics

Remarks on the formulation of quantum mechanics on noncommutative phase spaces

B. Muthukumar

Published Jan 18, 2007• 8 citations
arXivHTMLPDF
DOI
10.1088/1126-6708/2007/01/073

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The conceptual incompatibility of spacetime in gravity and quantum physics implies the existence of noncommutative spacetime and geometry on the Planck scale. We present the formulation of a noncommutative quantum mechanics based on the Seiberg–Witten map, and we study the Aharonov–Bohm effect induced by the noncommutative phase space. We investigate the existence of the persistent current in a nanoscale ring with an external magnetic field along the ring axis, and we introduce two observables to probe the signal coming from the noncommutative phase space. Based on this formulation, we give a value-independent criterion to demonstrate the existence of the noncommutative phase space.