Symmetry group at future null infinity II: Vector theory

Abstract

In this paper, we reduce the electromagnetic theory to future null infinity and obtain a vector theory at the boundary. We compute the Poincar\'e flux operators which could be generalized. We quantize the vector theory, and impose normal order on the extended flux operators. It is shown that these flux operators generate the supertranslation and superrotation. When working out the commutators of these operators, we find that a generalized electromagnetic duality operator should be included as the generators to form a closed symmetry algebra.