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In this paper we discuss one-dimensional models reproducing some features ofquantum electrodynamics and quantum chromodynamics at nonzero density andtemperature. Since a severe sign problem makes a numerical treatment of QED andQCD at high density difficult, such models help to explore various effectspeculiar to the full theory. Studying them gives insights into the largedensity behavior of the Polyakov loop by taking both bosonic and fermionicdegrees of freedom into account, although in one dimension only theimplementation of a global gauge symmetry is possible. For these models weevaluate the respective partition functions and discuss several observables aswell as the Silver Blaze phenomenon.

Simple QED- and QCD-like Models at Finite Density