Generic nondegenerate NCQM sectors with nonzero central character parameters are not unitarily equivalent to ordinary QM as representations of G_NC.
A comparative review of four formulations of noncommutative quantum mechanics
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abstract
Four formulations of quantum mechanics on noncommutative Moyal phase spaces are reviewed. These are the canonical, path-integral, Weyl-Wigner and systematic formulations. Although all these formulations represent quantum mechanics on a phase space with the same deformed Heisenberg algebra, there are mathematical and conceptual differences which we discuss.
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Central Characters of $G_{\mathrm{NC}}$, Darboux Normalization, and the Kinematical Inequivalence of NCQM and QM
Generic nondegenerate NCQM sectors with nonzero central character parameters are not unitarily equivalent to ordinary QM as representations of G_NC.