Positivity and Dense Matter

Deog Ki Hong and Stephen D.H. Hsu 1 Department of Physics, Pusan National University, Pusan 609-735, Korea [email protected] 2 Department of Physics, University of Oregon, Eugene OR 97403-5203 [email protected] (Dated: June 4, 2005) Abstract 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.