Coherent Distributions and Quantization

This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that the main difference between classical and quantum behavior arises from the coherence properties of the phase-space distributions known as "action waves" and Wigner functions. The quantum wave functions appear as elementary degrees of freedom for the phase space granularity.