Matching from an UV theory to a low-energy effective field theory can be done in more elegant and simpler ways than computing conventional Feynman diagrams. At one-loop level, the idea is to manipulate the functional determinant, which arises from evaluating the path integral, in a gauge-covariant way. As a result, one automatically arrives at gauge-invariant effective operators. In addition, much of the calculation can be done without referring to specific UV models, making it possible to obtain universal results in the form of widely-applicable master formulas.
I will give a pedagogical introduction to the basic ideas of gauge-covariant functional matching, and show how one can use "covariant diagrams," which may be thought of as gauge-covariant versions of Feynman diagrams, to keep track of such calculations.
