Quantum Off-Shell Recursion Relation

TL;DR

This paper develops a quantum off-shell recursion relation framework for loop-level scattering amplitudes in quantum field theories, extending classical recursion methods to include quantum corrections via Dyson-Schwinger equations.

Contribution

It introduces a novel quantum perturbiner expansion formalism that incorporates loop corrections and derives off-shell recursion relations using Dyson-Schwinger equations.

Findings

Reproduces one-loop six-point amplitudes in φ^4 theory

Provides recursion relations for loop-level correlation functions

Extends classical off-shell recursion to quantum level

Abstract

We construct off-shell recursion relations for arbitrary loop-level scattering amplitudes beyond the conventional tree-level recursion relations for $\phi^{4}$-theory and the Yang-Mills theory. We define a quantum perturbiner expansion that includes loop corrections from the quantum effective action formalism by identifying the external source. Our method clearly shows how the perturbiner expansion becomes an off-shell current generating function. 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 to arbitrary order of loop-level scattering amplitudes. We solve the recursion relation and reproduce the results which agree up to one-loop six-point scattering amplitudes for $\phi^{4}$-theory. Furthermore, we construct the recursions for computing loop-level correlation functions by replacing the choice of the external source.