  This paper applies $\zeta$-function regularization to evaluate the 1-loop
effective action for scalar field theories and Euclidean Maxwell theory in the
presence of boundaries. After a comparison of two techniques developed in the
recent literature, vacuum Maxwell theory is studied and the contribution of all
perturbative modes to $\zeta'(0)$ is derived: transverse, longitudinal and
normal modes of the electromagnetic potential, jointly with ghost modes. The
analysis is performed on imposing magnetic boundary conditions, when the
Faddeev-Popov Euclidean action contains the particular gauge-averaging term
which leads to a complete decoupling of all perturbative modes. It is shown
that there is no cancellation of the contributions to $\zeta'(0)$ resulting
from longitudinal, normal and ghost modes.
