Applying Gröbner Bases to Solve Reduction Problems for Feynman Integrals
نویسنده
چکیده
We describe how Gröbner bases can be used to solve the reduction problem for Feynman integrals, i.e. to construct an algorithm that provides the possibility to express a Feynman integral of a given family as a linear combination of some master integrals. Our approach is based on a generalized Buchberger algorithm for constructing Gröbner-type bases associated with polynomials of shift operators. We illustrate it through various examples of reduction problems for families of oneand two-loop Feynman integrals. We also solve the reduction problem for a family of integrals contributing to the three-loop static quark potential. E-mail: [email protected] E-mail: [email protected]
منابع مشابه
ar X iv : h ep - p h / 06 06 24 7 v 1 2 2 Ju n 20 06 S - bases as a tool to solve reduction problems for Feynman integrals
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 Gröbner bases. New results obtained with its help for a family of three-loop Feynman integrals are outlined.
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