  Zeta-function regularization is applied to complete a recent analysis of the
quantized electromagnetic field in the presence of boundaries. The quantum
theory is studied by setting to zero on the boundary the magnetic field, the
gauge-averaging functional and hence the Faddeev-Popov ghost field. Electric
boundary conditions are also studied. On considering two gauge functionals
which involve covariant derivatives of the 4-vector potential, a series of
detailed calculations shows that, in the case of flat Euclidean 4-space bounded
by two concentric 3-spheres, one-loop quantum amplitudes are gauge independent
and their mode-by-mode evaluation agrees with the covariant formulae for such
amplitudes and coincides for magnetic or electric boundary conditions. By
contrast, if a single 3-sphere boundary is studied, one finds some
inconsistencies, i.e. gauge dependence of the amplitudes.
