  We elaborate on previous results concerning the positivity of the Euclidean
path integral measure for low-energy modes in dense fermionic matter. We show
that the sign problem usually associated with fermions is absent if one
considers only low-energy degrees of freedom. We describe a method for
simulating dense QCD on the lattice and give a proof using rigorous
inequalities that the color-flavor locked (CFL) phase is the true vacuum of
three flavor, massless QCD. We also discuss applications to electronic systems
in condensed matter, such as generalized Hubbard models.
