  We consider local semitransparent Neumann boundary conditions for a quantum
scalar field as imposed by a quadratic coupling to a source localized on a flat
codimension-one surface. Upon a proper regularization to give meaning to the
interaction, we interpret the effective action as a theory in a first-quantized
phase space. We compute the relevant heat-kernel to all order in a homogeneous
background and to quadratic order in perturbations, giving a closed expression
for the corresponding effective action in $D=4$. In the dynamical case, we
analyze the pair production caused by a harmonic perturbation and by a Sauter
pulse. Notably, we prove the existence of a strong/weak duality that links this
Neumann field theory to the analogue Dirichlet one.
