Classical dynamics on three dimensional fuzzy space: Connecting the short and long length scales

Abstract

We derive the path integral action for a particle moving in three dimensional fuzzy space. From this we extract the classical equations of motion. These equations have rather surprising and unconventional features: They predict a cut-off in energy, a generally spatial dependent limiting speed, orbital precession remarkably similar to the general relativistic result, flat velocity curves below a length scale determined by the limiting velocity and included mass, displaced planar motion and the existence of two dynamical branches of which only one reduces to Newtonian dynamics in the commutative limit. These features place strong constraints on the non-commutative parameter and coordinate algebra to avoid conflict with observation and may provide a stringent observational test for this scenario of non-commutativity.

21 pages, 4 figures

References in corpus (5)

• Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
• String states, loops and effective actions in noncommutative field theory and matrix models
• Thermodynamics of a non-commutative fermion gas
• Spectrum of the three dimensional fuzzy well
• Scattering in three-dimensional fuzzy space

Cited by in corpus (4)

• Path integral action of a particle with the generalized uncertainty principle and correspondence with noncommutativity
• Path integral action in the generalized uncertainty principle framework
• Pinhole interference in three-dimensional fuzzy space
• Noncommutativity in Configuration Space Induced by A Conjugate Magnetic Field in Phase Space