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.

arXiv comment33 pages, 4 figures; v2: typos fixed and references added, published version

References in corpus (23)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• New Recursion Relations for Tree Amplitudes of Gluons
• New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
• On Tree Amplitudes in Gauge Theory and Gravity
• Bootstrapping Multi-Parton Loop Amplitudes in QCD
• Multigluon Helicity Amplitudes Involving a Quark Loop
• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
• On amplitudes in self-dual sector of Yang-Mills theory
• Berends-Giele recursion for double-color-ordered amplitudes
• Berends-Giele recursions and the BCJ duality in superspace and components
• One Loop Multiphoton Helicity Amplitudes
• Color/Kinematics Duality in AdS${}_4$
• Non-linear gauge transformations in $D=10$ SYM theory and the BCJ duality
• Perturbiner Methods for Effective Field Theories and the Double Copy
• Twofold Symmetries of the Pure Gravity Action
• Hidden Simplicity of the Gravity Action
• A solution to the non-linear equations of D=10 super Yang-Mills theory
• SD Perturbiner in YM+Gravity
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• Loop Amplitudes and Quantum Homotopy Algebras
• Gravitationally dressed Parke-Taylor amplitudes
• Multiparticle solutions to Einstein's equations
• Recursion Rules for Scattering Amplitudes in Non-Abelian Gauge Theories

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