Quantum and Classical Brackets

We describe p-mechanical (Kisil, V. V. (1996). Journal of Natural Geometry9(1), 1–14; Kisil, V. V. (1999). Advances in Mathematics147(1), 35–73; Prezhdo, O. V. and Kisil, V. V. (1997). Physical Review A56(1), 162–175) brackets that generate quantum (commutator) and classical (Poisson) brackets in corresponding representations of the Heisenberg group. We do not use any kind of semiclassical approximation or limiting procedure for ħ → 0