  We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3)
gauge theory and in full QCD as well as in quenched U(1) theory. As a measure
of the fluctuation properties of the eigenvalues, we consider the
nearest-neighbor spacing distribution. We find that in all regions of their
phase diagrams, compact lattice gauge theories have bulk spectral correlations
given by random matrix theory, which is an indication for quantum chaos. In the
confinement phase, the low-lying Dirac spectrum of these quantum field theories
is well described by random matrix theory, exhibiting universal behavior.
Related results for gauge theories with minimal coupling are now discussed also
in the chirally symmetric phase.
