  In this paper we discuss one-dimensional models reproducing some features of
quantum electrodynamics and quantum chromodynamics at nonzero density and
temperature. Since a severe sign problem makes a numerical treatment of QED and
QCD at high density difficult, such models help to explore various effects
peculiar to the full theory. Studying them gives insights into the large
density behavior of the Polyakov loop by taking both bosonic and fermionic
degrees of freedom into account, although in one dimension only the
implementation of a global gauge symmetry is possible. For these models we
evaluate the respective partition functions and discuss several observables as
well as the Silver Blaze phenomenon.
