EUCLIDEAN MAXWELL THEORY IN THE PRESENCE OF BOUNDARIES .2.

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 m agnetic field, the gauge-averaging functional, and hence the Faddeev-P opov ghost field. Electric boundary conditions are also studied. On co nsidering 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-sph eres, one-loop quantum amplitudes are gauge independent and their mode -by-mode evaluation agrees with the covariant formulae for such amplit udes and coincides for magnetic or electric boundary conditions. By co ntrast, if a single 3-sphere boundary is studied, one finds some incon sistencies, i.e. gauge dependence of the amplitudes.