World-line approach to the Bern-Kosower formalism in two-loop Yang-Mills theory Original Research Article

Based on the world-line formalism with a sewing method, we derive the Yang-Mills effective action in a form useful to generate the Bern-Kosower-type master formulae for gluon scattering amplitudes at the two-loop level. It is shown that four-gluon (φ4 type sewing) contributions can be encapsulated in the action with three-gluon (φ3 type) vertices only, the total action thus becoming a simple expression. We then derive a general formula for a two-loop Euler-Heisenberg type action in a pseudo-abelian su(2) also studied.