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Feynman integral reduction using Grobner bases
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DOI：10.1007/JHEP05(2023)168.png)
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Abstract
En 中文
We investigate the reduction of Feynman integrals to master integrals using Grobner bases in a rational double-shift algebra Y in which the integration-by-parts (IBP) relations form a left ideal. The problem of reducing a given family of integrals to master integrals can then be solved once and for all by computing the Grobner basis of the left ideal formed by the IBP relations. We demonstrate this explicitly for several examples. We introduce so-called first-order normal-form IBP relations which we obtain by reducing the shift operators in Y modulo the Grobner basis of the left ideal of IBP relations. For more complicated cases, where the Grobner basis is computationally expensive, we develop an ansatz based on linear algebra over a function field to obtain the normal-form IBP relations.
Keywords:
Differential and Algebraic Geometry
Higher-Order Perturbative Calculations
Non-Commutative Geometry
Journal
IF:
5.5
Papers:
3.9W
Citations:
13.7W
