Null hypersurface quantization, electromagnetic duality and asymptotic symmetries of Maxwell theory

TL;DR

This paper develops a regularization method for quantizing Maxwell theory at null infinity, enabling systematic analysis of boundary symmetries, charges, and dualities, with potential applications to broader theories.

Contribution

It introduces a controlled regularization approach for boundary quantization in Maxwell theory, facilitating the study of asymptotic charges and dualities in a systematic way.

Findings

Reproduces known operator algebras for boundary charges

Applies to BMS and large gauge transformations

Demonstrates electromagnetic duality charge generates expected transformations

Abstract

In this paper we consider introducing careful regularization in the quantization of Maxwell theory in the asymptotic null infinity. This allows systematic discussions of the commutators in various boundary conditions, and application of Dirac brackets accordingly in a controlled manner. This method is most useful when we consider asymptotic charges that are not localized at the boundary $u\to \pm \infty$ like large gauge transformations. We show that our method reproduces the operator algebra in known cases, and it can be applied to other space-time symmetry charges such as the BMS transformations. We also obtain the asymptotic form of the U(1) charge following from the electromagnetic duality in an explicitly EM symmetric Schwarz-Sen type action. Using our regularization method, we demonstrate that the charge generates the expected transformation of a helicity operator. Our method promises applications in more generic theories.