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In manifolds with spatial boundary, BRST formalism can be used to quantizegauge theories. We show that, in a $U(1)$ gauge theory, only a subset of allthe boundary conditions allowed by the self-adjointness of the Hamiltonianpreserves BRST symmetry. Hence, the theory can be quantized using BRSTformalism only when that subset of boundary conditions is considered. We alsoshow that for such boundary conditions, there exist fermionic states which arelocalized near the boundary.

BRST Symmetry: Boundary Conditions and Edge States in QED