We present the description of the exponentiated diagrams in terms of generating function within the universal diagrammatic technique. In particular, we show the exponentiation of the gauge theory amplitudes involving products of an arbitrary number of Wilson lines of arbitrary shapes, which generalizes the concept of web diagrams. The presented method gives a new viewpoint on the web diagrams and proves the non-Abelian exponentiation theorem.
We present the method to define web-diagrams on the operator level, using the functional integral and generating functions. The method allows one to obtain and investigate the exponentiated diagrams in the straightforward manner. Although, for the moment, the method does not result to any new information on web diagrams, it allows to obtain the known results in a simple and visual way.