Quantum Off-Shell Recursion Relation

Abstract

We construct off-shell recursion relations for arbitrary loop-level scattering amplitudes beyond the conventional tree-level recursion relations for ${\varphi }^4$-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 ${\varphi }^4$-theory. Furthermore, we construct the recursions for computing loop-level correlation functions by replacing the choice of the external source.

33 pages, 4 figures; v2: typos fixed and references added, published version

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• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
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Cited by in corpus (5)

• New recursions for tree-level correlators in (Anti) de Sitter space
• One-loop off-shell amplitudes from classical equations of motion
• Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents
• Perturbations of General Relativity to All Orders and the General $n^{\mathrm{th}}$ Order Terms
• Unfolded Dynamics Approach and Quantum Field Theory