Large Gauge Symmetries and Asymptotic States in QED

TL;DR

This paper explores how large gauge transformations in QED influence the structure of asymptotic states and the S-matrix, revealing that the soft photon theorem emerges from the choice of physical states.

Contribution

It demonstrates that large gauge transformations affect the asymptotic states in QED and clarifies their relation to the soft photon theorem and vacuum structure.

Findings

LGT charge is momentum-independent and linked to the vacuum.

Soft theorem arises from the use of physical asymptotic states.

Physical states include long-range electric fields between charges.

Abstract

Large Gauge Transformations (LGT) are gauge transformations that do not vanish at infinity. Instead, they asymptotically approach arbitrary functions on the conformal sphere at infinity. Recently, it was argued that the LGT should be treated as an infinite set of global symmetries which are spontaneously broken by the vacuum. It was established that in QED, the Ward identities of their induced symmetries are equivalent to the Soft Photon Theorem. In this paper we study the implications of LGT on the S-matrix between physical asymptotic states in massive QED. In appose to the naively free scattering states, physical asymptotic states incorporate the long range electric field between asymptotic charged particles and were already constructed in 1970 by Kulish and Faddeev. We find that the LGT charge is independent of the particles' momenta and may be associated to the vacuum. The soft theorem's manifestation as a Ward identity turns out to be an outcome of not working with the physical asymptotic states.