The infrared triangle in the context of IR safe S matrices
Mischa Panchenko
TL;DR
The paper reframes the infrared triangle in massless QFT within an infrared-safe S-matrix, arguing that non-trivial asymptotic dynamics render soft emissions decoupled and the theory free of infrared divergences. It shows that soft decoupling, large-gauge transformation charges, and memory are connected via the asymptotic current $J_\mu^{as}$ and the dressing operator $R(t)$. Key contributions include a refined derivation of LGT charges in this IR-safe framework, a direct link to memory, and a unified treatment that applies to gravity and other massless theories. Memory in IR-safe theories arises from asymptotic field expectations rather than soft-emission probabilities, and antipodal matching follows from decoupling, yielding a complete infrared tetrahedron.
Abstract
In the present note we show that the recently established connections between soft theorems, large gauge transformations and memories are persistant in the infrared safe formulation of quantum field theory. They take a different and simplified form and can all be derived from the non-trivial asymptotic dynamics that is proper to any theory with massless fields. Several results in this paper had already been presented in one form or another with varying interpretations. The new parts here are an improved derivation of charges for large gauge transformations in the framework of non-trivial asymptotic dynamics, the connection to the classical memory effect and an overall more unified and accessible treatment of the topic. Since the formulation of QFT without infrared divergences is physically more appealing, the infrared safe version of the above connections should be so as well.