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A practical criterion of irreducibility of multi-loop Feynman integrals. (English) Zbl 1247.81314
Summary: A practical criterion for the irreducibility (with respect to integration by part identities) of a particular Feynman integral to a given set of integrals is presented. The irreducibility is shown to be related to the existence of stable (with zero gradient) points of a specially constructed polynomial.

##### MSC:
 81T18 Feynman diagrams
##### Keywords:
irreducibility of Feynman integrals
Full Text:
##### References:
 [1] Chetyrkin, K.G.; Tkachov, F.V.; Tkachov, F.V., Nucl. phys. B, Phys. lett. B, 100, 65, (1981) [2] Broadhurst, D.J.; Avdeev, L.V.; Tarasov, O.V.; Tarasov, O.V.; Smirnov, V.A.; Veretin, O.L.; Anastasiou, C.; Gehrmann, T.; Oleari, C.; Remiddi, E.; Tausk, J.B.; Smirnov, A.V.; Smirnov, V.A., Z. phys. C, Comput. phys. commun., Nucl. phys. B, Acta phys. Pol. B, Nucl. phys. B, Nucl. phys. B, 580, 577, (2000) [3] Laporta, S.; Remiddi, E.; Mastrolia, P.; Remiddi, E., Phys. lett. B, Nucl. phys. B (proc. suppl.), 89, 76, (2000) [4] Baikov, P.A., Phys. lett. B, 474, 385, (2000) [5] Baikov, P.A.; Baikov, P.A., Phys. lett. B, Nucl. instrum. methods A, 389, 347, (1997) [6] Baikov, P.A.; Smirnov, V.A., Phys. lett. B, 477, 367, (2000) [7] Fleischer, J.; Kalmykov, M.Yu.; Kotikov, A.V., Phys. lett. B, 462, 169, (1999)
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