Origin of negative values of the Wigner distribution function

The classical limit of the quantum Wigner distribution function is found to be either the classically defined Wigner distribution function or a perfectly localized phase space distribution of interacting classical particles/optical rays. In the first case the negative values of the Wigner distribution function are shown to be due to the nonlocal character of the wave field and are not a signature of the non-classical quantum states. The second case shows that the hidden assumption of interacting particles/rays, not explicit in the quantum formulation, is a consequence of the nonlocal character of the quantum wavefunction.