Pinched Gluon Vertex Operator in Super-Worldline Formalism

We reformulate, using super worldline formalism, the pinched gluon vertex operator proposed by Strassler. The pinched vertex operator turns out to be the product of two gluon vertex operators with the insertion of $\delta$-function which makes the super distances between them zero. Thus the pinch procedures turn out to be nothing but the insertions of $\delta$-function. Applying our formulation to two-loop diagrams which are the QED correction to gluon scatterings via a single spinor loop, with the QED charge e being replaced by the strong coupling g, we show various formulae on pinched N-point functions.