Parameters of noncommutativity in Lie-algebraic noncommutative space

Abstract

We find condition on the parameters of noncommutativity on which a list of important results can be obtained in a space with Lie-algebraic noncommutativity. Namely, we show that the weak equivalence principle is recovered in the space, the Poisson brackets for coordinates and momenta of the center-of-mass of a composite system do not depend on its composition and reproduce relations of noncommutative algebra for coordinates and momenta of individual particles if parameters of noncommutativity corresponding to a particle are proportional inversely to its mass. In addition in particular case of Lie-algebraic noncommutativity (space coordinates commute to time) on this condition the motion of the center-of-mass is independent of the relative motion and problem of motion of the center-of-mass and problem corresponding to the internal motion can be studied separately.

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Cited by in corpus (7)

• Energy-dependent noncommutative quantum mechanics
• Upper bound on the momentum scale in noncommutative phase space of canonical type
• Macroscopic body in Snyder space and minimal length estimation
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Minimal length estimation on the basis of studies of the Sun-Earth-Moon system in deformed space
• Kinetic energy properties and weak equivalence principle in a space with GUP
• Features of description of composite system's motion in twist-deformed space-time