On Noncommutative Classical Mechanics

Abstract

In this work, I investigate the noncommutative Poisson algebra of classical observables corresponding to a proposed general Noncommutative Quantum Mechanics, \cite{1}. I treat some classical systems with various potentials and some Physical interpretations are given concerning the presence of noncommutativity at large scales (Celeste Mechanics) directly tied to the one present at small scales (Quantum Mechanics) and its possible relation with UV/IR mixing.

14 pages, 0 figures

References in corpus (5)

• Noncommutative Quantum Mechanics from Noncommutative Quantum Field Theory
• Two phases of the noncommutative quantum mechanics
• Quantum Mechanics on the Noncommutative Torus
• The Kepler problem and non commutativity
• Noncommutative Quantum Mechanics and rotating frames

Cited by in corpus (19)

• Composite system in noncommutative space and the equivalence principle
• Weak equivalence principle in noncommutative phase space and the parameters of noncommutativity
• Quantum gravity, minimum length and Keplerian orbits
• Non-commutative black holes of various genera in the connection formalism
• Upper bound on the momentum scale in noncommutative phase space of canonical type
• Noncommutative Mapping from the symplectic formalism
• Kinematic variables in noncommutative phase space and parameters of noncommutativity
• Noncommutative phase space with rotational symmetry and hydrogen atom
• Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle
• Noncommutative Brownian motion
• Influence of noncommutativity on the motion of Sun-Earth-Moon system and the weak equivalence principle
• Accelerating cosmologies in an integrable model with noncommutative minisuperspace variables
• Minimal momentum estimation in noncommutative phase space of canonical type with preserved rotational and time reversal symmetries
• Some singular spacetimes and their possible alternatives
• Thermostatistical analysis and negative heat capacities of Yukawa and Lee-Wick potentials in noncommutative phase spaces
• Non-Commutative fluid: an alternative source of cosmic acceleration
• Snyder Like Modified Gravity in Newton's Spacetime
• (Pre)-Inflationary Dynamics with Starobinsky Potential in Noncommutative Effective LQC
• Vlasov-Klimontovich Equation in Action