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Determining Feynman integrals with only input from linear algebra

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arxiv 2201.11637 v3 pith:4FRBLMGB submitted 2022-01-27 hep-ph hep-th

Determining Feynman integrals with only input from linear algebra

classification hep-ph hep-th
keywords linearfeynmanintegralsloopsalgebraalgebraicbyproductcalculate
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We find that all Feynman integrals (FIs), having any number of loops, can be completely determined once linear relations between FIs are provided. Therefore, FIs computation is conceptually changed to a linear algebraic problem. Examples up to 5 loops are given to verify this observation. As a byproduct, we get a powerful method to calculate perturbative corrections in quantum field theory.

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