Sub-leading Soft Photons and Gravitons

Soft factorization has been shown to hold to sub-leading order in QED and to sub-sub-leading order in perturbative quantum gravity, with various loop and non-universal corrections that can be found. In a recent paper, we show that all terms factorizing at tree level can be uniquely identified as boundary terms that exist already in the classical expressions for the electric current and stress tensor of a point particle. Further, it turns out that one cannot uniquely identify such boundary terms beyond the sub-leading or sub-sub-leading orders respectively, providing evidence that the factorizability of the tree level soft factor only holds to these orders. In this talk, I will first introduce and motivate the soft theorems, and then explain our recent results. I'll also show how our new classical intuition is reflected in the calculation of quantum scattering amplitudes.