Quark Confinement in Unusual Environments

We consider the properties of l-dimensional gauge field-theories at finite temperatures and densities. The massive Schwinger model in the presence of a uniform charge background is shown to form a Wigner crystal which Debye screens charged impurities. The two species Schwinger model with oppositely charged fermions is studied at finite baryon density. This system does not undergo a phase transition as the density is increased, but becomes progressively more polarizable until at infinite density Debye screening occurs. Finally we consider the massive Schwinger model at non-zero temperature and show that Debye screening occurs at infinite temperature. We speculate that in three dimensions this last transition occurs at finite temperature.