BRST Symmetry: Boundary Conditions and Edge States in QED

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.

15 pages, Minor corrections

References in corpus (3)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Casimir Effect and Global Theory of Boundary Conditions

Cited by in corpus (4)

• Dynamical edge modes in Maxwell theory from a BRST perspective, with an application to the Casimir energy
• Aspects of Boundary Conditions for Nonabelian Gauge Theories
• Matrix Model of QCD: Edge Localized Glue Balls and Phase Transitions
• Edge states and anomalous SUSY in (2+1)-dimensional Maxwell Chern-Simons theory