Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals

2008/04/30 by Roman N. Lee, R. N. Lee · 6 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic number #Algebraic structure #Black Holes and Theoretical Physics #Classical mechanics #Geometry #Group (periodic table) #Identity (music) #Lie group #Lorentz group #Lorentz transformation #Mathematical analysis #Mathematics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Reduction (mathematics) #hep-ph

paper · pdf · doi:10.1088/1126-6708/2008/07/031

published as JHEP0807:031,2008 · 6 pages, RevTeX. Version, published in JHEP, references corrected

openalex publication_date 2008/07/08 · arxiv created 2008/08/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The excessiveness of integration-by-part (IBP) identities is discussed. The Lie-algebraic structure of the IBP identities is used to reduce the number of the IBP equations to be considered. It is shown that Lorentz-invariance (LI) identities do not bring any information additional to that contained in the IBP identities, and therefore, can be discarded.

Citations

• Integration by parts: The algorithm to calculate β-functions in 4 loops
• Differential Equations for Two-Loop Four-Point Functions

Cited by

• Space–time dimensionality D as complex variable: Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D
• Complete reduction of integrals in two-loop five-light-parton scattering amplitudes *
• INTEGRATION BY PARTS: AN INTRODUCTION
• Reinforcement Learning and Metaheuristics for Feynman Integral Reduction
• Dual conformal symmetry, integration-by-parts reduction, differential equations, and the nonplanar sector
• Numerator seagull and extended Symmetries of Feynman Integrals