Quantum Smoothening of ‘Classical Anomaly’

Quantum smoothening of a classical anomaly is studied and will be presented for a special situation (ℝ2). In classical physics, in the sense of Poisson brackets, a function of p and a function of q never commute (except for constant functions). We shall characterize an infinite family of such functions which do not commute in the classical system but do commute in the quantum system. We utilize this fact to construct a toy model for an integrable system. Quantum description of the model leads to infinitely many conservation laws.