Comments on Symmetry Operators, Asymptotic Charges and Soft Theorems

TL;DR

This paper explores the connection between emergent 1-form symmetries and soft photon theorems in QED, revealing how these symmetries underpin conserved charges and influence scattering amplitudes.

Contribution

It demonstrates that electric and magnetic 1-form symmetries in QED lead to an algebra of conserved charges, linking soft theorems to asymptotic symmetries and scattering contact terms.

Findings

Identifies 1-form symmetries in HQET and SCET regimes.

Shows these symmetries produce an algebra with a central extension.

Connects the algebra to soft photon theorems and scattering amplitude contact terms.

Abstract

We study the relation between emergent 1-form symmetries and soft photon theorems in QED. We show that in the relevant massive and massless kinematic regimes, described respectively by HQET and SCET, the soft sector admits electric and magnetic 1-form symmetries. We then show that these symmetries give rise to an infinite-dimensional Abelian algebra of ordinary conserved charges, with a central extension. In Minkowski spacetime, suitable choices of hypersurfaces reduce these charges to the familiar asymptotic symmetry charges and imply the leading electric and magnetic soft photon theorems. We further show that the central term in this algebra fixes a contact term appearing in scattering amplitudes involving two soft photons with mixed electric-magnetic polarizations. Finally, we extend the same construction to inclusive observables and apply it to QED photon detectors.