A guide to functional methods beyond one-loop order - Javier Fuentes-Martín; Adrián Moreno-Sánchez; Ajdin Palavrić; Anders Eller Thomsen (Journal of High Energy Physics)
Abstract Functional methods can be applied to the quantum effective action to efficiently determine counterterms and matching conditions for effective field theories. We extend the toolbox to two-loop order and beyond and show how to evaluate the expansion of the path integral in a manifestly gauge-covariant manner. We also generalize the method to theories with mixed spin statistics and prove the validity of the hard-region matching formula to all loop orders. The methods are exemplified with a two-loop matching calculation of the Euler–Heisenberg Lagrangian resulting from decoupling the electron in QED.