A Minimal Framework for Non-Commutative Quantum Mechanics
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- Hurley, D.J. & Vandyck, M.A. Found Phys (2014) 44: 1168. doi:10.1007/s10701-014-9835-8
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Deformation quantisation is applied to ordinary Quantum Mechanics by introducing the star product in a configuration space combining a Riemannian structure with a Poisson one. A Hilbert space compatible with such a configuration space is designed. The dynamics is expressed by a Hermitian Hamiltonian containing a scalar potential and a one-form potential. As a simple illustration, it is shown how a particular type of non-commutativity of the star product is interpretable as generating the Zeeman effect of ordinary Quantum Mechanics.