Local Neumann semitransparent layers: Resummation, pair production, and duality

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