Loop Amplitudes and Quantum Homotopy Algebras
Branislav Jurčo, Tommaso Macrelli, Christian Sämann, Martin Wolf
Abstract
A bstract We derive a recursion relation for loop-level scattering amplitudes of La- grangian field theories that generalises the tree-level Berends-Giele recursion relation in Yang-Mills theory. The origin of this recursion relation is the homological perturbation lemma, which allows us to compute scattering amplitudes from minimal models of quantum homotopy algebras in a recursive way. As an application of our techniques, we give an alternative proof of the relation between non-planar and planar colour-stripped scattering amplitudes.
Topics & Concepts
Recursion (computer science)PhysicsScattering amplitudeHomotopyQuantum field theoryScatteringPerturbation theory (quantum mechanics)Loop (graph theory)AmplitudeQuantumPlanarMathematical physicsMinimal modelsPerturbation (astronomy)Relation (database)Topological quantum field theoryPure mathematicsField (mathematics)Gauge theoryScattering theoryQuantum mechanicsS-matrixDouble recursionAlgebra over a fieldQuantum electrodynamicsHomotopy lifting propertyPath integral formulationQuantum affine algebraTheoretical physicsTopological quantum numberRiemann surfaceAlgebraic structures and combinatorial modelsBlack Holes and Theoretical PhysicsHomotopy and Cohomology in Algebraic Topology