Large gauge transformation and little group for soft photons

TL;DR

The paper clarifies the relationship between large gauge transformations (LGT) at null infinity and the little group of massless photons. By expressing LGT charges in QED in terms of the non-compact ISO(2) generators $\Pi_1$ and $\Pi_2$, it shows that LGT is equivalent to a gauged realization of the little group, with degenerate soft-photon vacua labeled by continuous eigenvalues of the LGT charge $Q$. The authors construct the LGT representation on soft states, linking the vacuum structure to ISO(2) algebra and demonstrating that the scalar-function and operator descriptions of gauge transformations are two faces of the same boundary symmetry. This work provides a unified symmetry framework for soft theorems and memory effects, and suggests analogous ISO(2) structures may appear in gravitational LGT and related continuous-spin representations.

Abstract

Recently, large gauge transformation (LGT), the residual gauge symmetry after gauge fixing that survives at null infinity, has drawn much attention concerning soft theorems and the memory effect. We point out that LGT charges in quantum electrodynamics are in fact one of non-compact generators of the two dimensional Euclidean group. Moreover, by comparing two equivalent descriptions of gauge transformation, we suggest that LGT is simply another way of describing the gauged little group for massless soft photons.