•Soft photons

To find the contribution of emission of one soft photon to a given process, we must multiply the tree-order amplitude with the factor from Weinberg (13.1.1)-(13.1.2) and integrate over q from zero to the cutoff.

The factor reads:

(CouplingConstant[QED[1], RenormalizationState[0]] Pair[LorentzIndex[μ1], Momentum[q]])/(Pair[Momentum[p], Momentum[q]] + I SmallEpsilon)

(e^(0  ) q^μ _ 1)/(i ϵ + p  ·  q)

where a summation over p (p1,p2,...) for all external electrons is understood, and q is the momentum of the emitted photon.


Converted by Mathematica  (July 10, 2003)