Newton's second law in a non-commutative space

Abstract

In this Letter we show that corrections to Newton's second law appear if we assume a symplectic structure consistent with the commutation rules of the non-commutative quantum mechanics. For central field we find that the correction term breaks the rotational symmetry. For the Kepler problem, this term is similar to a Coriolis force. © 2003 Elsevier Science B.V. All rights reserved.