S-bases as a tool to solve reduction problems for Feynman integrals

2006/06/22 by A. V. Smirnov, A.V. Smirnov, V. A. Smirnov +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Cryptography and Residue Arithmetic #Polynomial and algebraic computation #hep-ph

paper · pdf · doi:10.1016/j.nuclphysbps.2006.09.032

published as Nucl.Phys.Proc.Suppl.160:80-84,2006 · 5 pages, uses espcrc2.sty

arxiv created 2006/06/22 · openalex publication_date 2006/10/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We suggest a mathematical definition of the notion of master integrals and present a brief review of algorithmic methods to solve reduction problems for Feynman integrals based on integration by parts relations. In particular, we discuss a recently suggested reduction algorithm which uses Groebner bases. New results obtained with its help for a family of three-loop Feynman integrals are outlined.

Citations

• Differential Equations for Two-Loop Four-Point Functions
• Explicit solutions of the 3-loop vacuum integral recurrence relations

Cited by

• Reinforcement Learning and Metaheuristics for Feynman Integral Reduction