  An investigation of classical chaos and quantum chaos in gauge fields and
fermion fields, respectively, is presented for (quantum) electrodynamics. We
analyze the leading Lyapunov exponents of U(1) gauge field configurations on a
$12^3$ lattice which are initialized by Monte Carlo simulations. We find that
configurations in the strong coupling phase are substantially more chaotic than
in the deconfinement phase. Considering the quantum case, complete eigenvalue
spectra of the Dirac operator in quenched 4d compact QED are studied on $8^3
\times 4$ and $8^3 \times 6$ lattices. We investigate the behavior of the
nearest-neighbor spacing distribution $P(s)$ as a measure of the fluctuation
properties of the eigenvalues in the strong coupling and the Coulomb phase. In
both phases we find agreement with the Wigner surmise of the unitary ensemble
of random-matrix theory indicating quantum chaos.
