Abstract
We derive generalized sheet transition conditions for electromagnetism on the joint domain of physical and observation states. Variation of a common bulk and surface action gives $n_I[\mathscr H^{IB}]+D_Ap^{AB}=K^B$, with observation-direction transport included in the surface balance. A gauge-invariant action with two potential traces supplies the complementary curvature-jump condition. Ordinary Maxwell sheet theory follows when the constitutive operators and boundary data preserve the physical electromagnetic sector. For a minimally coupled projector field, fixed endpoint data on an observation interval select a stable equilibrium with local response $c(s)=d[1-\cos(\pi s/\ell)]$. This profile generates an infinite tridiagonal coupling matrix: the relative couplings are determined by the equilibrium, while $d$ remains a material parameter. The resulting weak-field scattering problem conserves power and admits an analytic truncation bound at channel thresholds. The underlying nonlinear equations retain the field-induced displacement of the projector. A separate finite-rank response gives an exactly closed two-mode problem and permits controlled finite-layer and causal dispersive realizations. In identical half-spaces, both continuous-trace models have a one-sided total conversion bound of one half. Eliminating unresolved observation modes produces an ordinary effective admittance, establishing the need for independently calibrated preparation and readout of observation modes when interpreting scattering measurements.