Finite density lattice gauge theories with positive fermion determinants

We perform simulations of (3-colour) QCD with 2 quark flavours at a finite chemical potential μI for isospin (I3), and of 2-colour QCD at a finite chemical potential μ for quark number. At zero temperature, QCD at finite μI has a mean-field phase transition at μI = mπ to a superfluid state with a charged pion condensate which spontaneously breaks I3. We study the finite temperature transition as a function of μI. For μI < mπ, where this is closely related to the transition at finite μ, this appears to be a crossover independent of quark mass, with no sign of the proposed critical endpoint. For μI > mπ this becomes a true phase transition where the pion condensate evaporates. For μI just above mπ the transition seems to be second order, while for larger μI it appears to become first order. At zero temperature, 2-colour QCD also possesses a superfluid state with a diquark condensate. We study its spectrum of Goldstone and pseudo-Goldstone bosons associated with chiral and quark-number symmetry breaking. (author)