Noncommutative Classical Mechanics

In this work, I investigate the noncommutative Poisson algebra of classical observables corresponding to a proposed general noncommutative quantum mechanics, Djemai, A. E. F. and Smail, H. (2003). I treat some classical systems with various potentials and some physical interpretations are given concerning the presence of noncommutativity at large scales (celestial mechanics) directly tied to the one present at small scales (quantum mechanics) and its possible relation with UV/IR mixing.