Determining Feynman Integrals with Only Input from Linear Algebra
Zhi-Feng Liu, Yan-Qing Ma
Abstract
We find that all Feynman integrals (FIs), having any number of loops, can be completely determined once linear relations between FIs are provided. Therefore, FI computation is conceptually changed to a linear algebraic problem. Examples up to five loops are given to verify this observation. As a by-product, we obtain a powerful method to calculate perturbative corrections in quantum field theory.
Topics & Concepts
Feynman diagramFeynman integralComputationAlgebraic numberQuantum field theoryProduct (mathematics)Algebra over a fieldField (mathematics)Linear algebraPhysicsMathematical physicsMathematicsPure mathematicsMathematical analysisAlgorithmGeometryNoncommutative and Quantum Gravity TheoriesBlack Holes and Theoretical PhysicsAlgebraic and Geometric Analysis