We discuss off-shell recursion relations for arbitrary loop-level scattering amplitudes beyond the conventional tree-level recursion relations. We define a quantum perturbiner expansion that includes loop corrections from the quantum effective action formalism. Instead of using the classical equations of motion in the conventional perturbiner method, we exploit the Dyson–Schwinger equation to derive the quantum off-shell recursion relation. Furthermore, we construct the recursions for computing loop-level correlation functions by replacing the choice of the external source.
