In this talk I will present recent results on description of the asymptotic (i.e. infrared) structure in quantum field theories with long-range interaction (e.g. QED). I will argue that the BFV formalism, traditionally applied to describe models on manifolds with boundary, is a natural framework to treat "the bounadry at infinity" as well. This could potentially be applied to soft modes in QED and gravity. The talk is based on joint work with Michele Schiavina.