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Algebraic algorithms for multiloop calculations. The first 15 years. What's next?

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arxiv hep-ph/9609429 v2 pith:GTB7NAEV submitted 1996-09-21 hep-ph hep-th

Fyodor V. Tkachov (INR Russ. Acad. Sci. , Moscow) This is my paper · ORCID
classification hep-phhep-th
keywords algebraicalgorithmscalculationsmultiloopbehindconceptcorrespondingexist
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The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the corresponding Feynman-parametrized integrands into a form that is optimal for numerical integration, with all the poles in D-4 explicitly extracted.

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  1. Quantum de Sitter Entropy and Sphere Partition Functions: A-Hypergeometric Approach to Higher Loop Corrections

    hep-th 2024-11 conditional novelty 6.0 of 10

    Scalar and vector Feynman integrals on the sphere are mapped to A-hypergeometric (GKZ) systems via embedding space propagators, enabling algorithmic higher-loop computations.

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