  In scenarios where electrons are confined to a flat surface, such as
graphene, quantizing electrodynamics reveals intriguing insights. We find that
one of Maxwell's equations manifests as part of the Hamiltonian, leading to
novel constraints on physical states due to residual gauge invariance. We
identify two quantum states with zero energy expectation values: one replicates
the scattering and absorption of light, a phenomenon familiar in classical
optics, while the other is more fundamentally associated with photon creation.
These states form an inseparable two-state system, giving a new formula for
reflection and transmission coefficients with photon emission effects. Notably,
there exists a special thickness of the surface where these states decouple,
offering intriguing possibilities for exploring physics through symmetry-based
perturbations involving concepts of parity, axial gauge fields, and surface
deformation.
