Complex Probability Distributions: A Solution for the Long-Standing Problem of QCD at Finite Density

We show how the prescription of taking the absolute value of the fermion determinant in the integration measure of QCD at finite density, forgetting its phase, reproduces the correct thermodynamical limit. This prescription, which applies also to other gauge theories with non-positive-definite integration measure, also has the advantage of killing finite size effects due to extremely small mean values of the cosine of the phase of the fermion determinant. We also give an explanation for the pathological behaviour of quenched QCD at finite density.