Infrared Divergences in QED, Revisited
(21 pages)

Vanishing S matrix elements in QED are often attributed to 'IR divergences' which are cancelled by tracing over soft photons. Here, it is argued that `zero' can be thought of as the correct transition probability when initial and final vacua are considered fixed (as is often the case), because this necessarily violates conservation laws associated with large gauge transformations. By allowing the final vacuum to be different to the initial vacuum, an IR finite result is obtained, and agrees with conventional treatments, but with a new (perhaps clearer) physical interpretation.

While the mathematical construction of such IR finite scattering amplitudes was carried out in 1970 by FaddeevKulish [Teor. Mat. Fiz. 4, 153 (1970)] and others, it was interpreted as the dressing of charges by clouds of soft photons. With the modern understanding of soft particles and asymptotic symmetries, the contribution of the soft photon cloud can be reinterpreted as the contribution of transitions between the degenerate vacua (related by large gauge transformations).
