Quark confinement in unusual environments

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Abstract
We consider the properties of one-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 nonzero temperature and show that Debye screening occurs at infinite temperature. We speculate that in three dimensions this last transition occurs at finite temperature.