Time symmetric Bloch-Nordsieck infrared cancellation

Abstract

It is usually assumed that the infrared divergences that occur for virtual photons in Feynman diagrams cancel against the corresponding divergences in phase space integrals for the emission of real soft photons. If this were the case then why do the corresponding phase space integrals for the absorption of real soft photons not diverge too, as one might expect on grounds of time-reversal symmetry, and if so what cancels these divergences? We show that this apparent time asymmetry is an artifact of the way that the diagrams are calculated, and we introduce a procedure for such calculations that is manifestly time symmetric. Moreover, we show that it is not mathematically meaningful to distinguish arbitrarily soft massless particles of positive and negative energy.