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- W2950041736 abstract "We are interested in the similarities and differences between the quantum-classical (Q-C) and the noncommutative-commutative (NC-Com) correspondences. As one useful platform to address this issue we derive the superstar Wigner-Moyal equation for noncommutative quantum mechanics (NCQM). A superstar $bigstar$-product combines the usual phase space $ast$ star and the noncommutative $star$ star-product. Having dealt with subtleties of ordering present in this problem we show that the classical correspondent to the NC Hamiltonian has the same form as the original Hamiltonian, but with a non-commutativity parameter $theta$-dependent, momentum-dependent shift in the coordinates. Using it to examine the classical and the commutative limits, we find that there exist qualitative differences between these two limits. Specifically, if $theta neq 0$ there is no classical limit. Classical limit exists only if $theta to 0$ at least as fast as $hbar to 0$, but this limit does not yield Newtonian mechanics, unless the limit of $theta/hbar$ vanishes as $theta to 0$. Another angle to address this issue is the existence of conserved currents and the Noether's theorem in the continuity equation, and the Ehrenfest theorem in the NCQM context." @default.
- W2950041736 created "2019-06-27" @default.
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- W2950041736 date "2005-04-19" @default.
- W2950041736 modified "2023-09-27" @default.
- W2950041736 title "The Classical and Commutative Limits of noncommutative Quantum Mechanics: A Superstar bigstar Wigner-Moyal Equation" @default.
- W2950041736 hasPublicationYear "2005" @default.
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