On the spacetime structure of infrared divergencies in QED

Abstract

We investigate analytic properties of string-integrated massless correlation functions and propagators with emphasis on their infrared behaviour. These are relevant in various models of quantum field theory with massless fields, including QED.

Infraparticle quantum fields and the formation of photon clouds

“…Vertex operators V qc (x) are string-localized in the spacelike cones x + e∈supp(c) R + e. In general, they commute up to a phase [40,65]. In particular, whenever the (smeared) strings x i + e∈supp(c i ) R + e are spacelike separated, the phase is zero and the fields commute.…”

“…The same strategy applied to the vertex operators in section 3.1.1 in four dimensions seems promising at first sight: the power law factors in (3.10) also produce a complex phase (proportional to the product of charges and the bilinear form c, c in (A. 19)) -but the homogeneous functions H in the vertex operator correlations contribute another factor [40]. This factor being possibly of modulus > 1, jeopardizes the interpretation of the computed quantity as a scattering amplitude.…”

“…where 1 (x 2 ) − is the distributional limit lim ε↓0 String-integrated correlation functions in position space were computed in [40] for spacelike e. One string integration is easily performed as an elementary integral s = s + (xe)…”

“…Eq. (A.12) with two purely spatial strings (e 0 = e 0 = 0) has been computed in [40]. The result is symmetric in e 1 = e ↔ e 2 = −e .…”

“…Two-point functions of the string-localized potential A µ (e) involve only derivatives of (A.13). The derivative is IR regular, and takes a much simpler and highly symmetric form [40]:…”