  The quark propagator is calculated in the Nambu-Jona-Lasinio (NJL) model in a
self-consistent 1/Nc-expansion at next-to-leading order. The calculations are
carried out iteratively in Euclidean space. The chiral quark condensate and its
dependence on temperature and chemical potential is calculated directly and
compared with the mean-field results. In the chiral limit, we find a
second-order phase transition at finite temperature and zero chemical
potential, in agreement with universality arguments. At zero temperature and
finite chemical potential, the phase transition is first order. In comparison
with the mean-field results, the critical temperature and chemical potential
are slightly reduced. We determine spectral functions from the Euclidean
propagators by employing the Maximum-Entropy-Method (MEM). Thereby quark and
meson masses are estimated and decay channels identified. For testing this
method, we also apply it to evaluate perturbative spectral functions, which can
be calculated directly in Minkowski space. In most cases we find that MEM is
able to reproduce the rough features of the spectral functions, but not the
details.
