BRST Symmetry: Boundary Conditions and Edge States in QED

TL;DR

This paper investigates how BRST symmetry constrains boundary conditions in U(1) gauge theories on manifolds with boundaries, revealing the existence of boundary-localized fermionic states under symmetry-preserving conditions.

Contribution

It identifies the specific boundary conditions compatible with BRST symmetry in gauge theories and demonstrates the existence of boundary-localized fermionic states.

Findings

Only a subset of boundary conditions preserve BRST symmetry.

Boundary-localized fermionic states exist under these conditions.

Quantization is consistent only with symmetry-preserving boundary conditions.

Abstract

In manifolds with spatial boundary, BRST formalism can be used to quantize gauge theories. We show that, in a $U(1)$ gauge theory, only a subset of all the boundary conditions allowed by the self-adjointness of the Hamiltonian preserves BRST symmetry. Hence, the theory can be quantized using BRST formalism only when that subset of boundary conditions is considered. We also show that for such boundary conditions, there exist fermionic states which are localized near the boundary.