Quantum off-shell recursion relation

A bstract We construct off-shell recursion relations for arbitrary loop-level scattering amplitudes beyond the conventional tree-level ϕ 4 -theory and Yang-Mills theory. define a quantum perturbiner expansion that includes loop corrections from effective action formalism by identifying external source. Our method clearly shows how becomes an current generating function. Instead of using classical equations motion in method, we exploit Dyson-Schwinger equation to derive relation order amplitudes. solve reproduce results which agree up one-loop six-point -theory. Furthermore, recursions computing correlation functions replacing choice