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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, 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.

Determining Feynman integrals with only input from linear algebra

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, 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.
Paper Structure (21 equations, 1 figure)

This paper contains 21 equations, 1 figure.

Figures (1)

  • Figure 1: Some typical Feynman diagrams of single-mass vacuum FIs up to 5 loops, where solid lines denote massive propagators, dotted lines denote massless propagators.