On the reduction of Feynman integrals to master integrals

Abstract

The reduction of Feynman integrals to master integrals is an algebraic problem that requires algorithmic approaches at the modern level of calculations. Straightforward applications of the classical Buchberger algorithm to construct Groebner bases seem to be inefficient. An essential modification designed especially for this problem has been worked out. It has been already applied in two- and three-loop calculations. We are also suggesting to combine our method with the Laporta's algorithm.

8 pages, proceedings of ACAT07

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• Studies of low-energy effective actions in supersymmetric field theories
• Tensor structure from scalar Feynman matroids
• Landau's Last Paper and its Impact on Developments in Mathematics, Physics and Other Disciplines in New Millennium
• Applying Mellin-Barnes technique and Groebner bases to the three-loop static potential