Functional Formalism for the Infrared Problem
In the asymptotic limit for scalar QED the boson current operator can be approximated by a current operator whose eigenvalue corresponds to the classical current of a point-charge moving with constant velocity. Using this approximation in the Gell-Mann-Low formula we obtain a path-ordered phase factor which multiplies the free boson propagator (Prog. Theor. Phys. 93, 1105). This coincides with the Bloch-Nordsieck propagator in the WKB approximation. Instead, we can substitute the classical current in the complete generating functional and first integrate over the gauge fields. This illustrates the usefulness of functional techniques for tackling the IR problem and we propose a similar construct to QCD and quantum gravity.