Letters in Mathematical Physics

, Volume 97, Issue 1, pp 37–44 | Cite as

The Number of Master Integrals is Finite



For a fixed Feynman graph one can consider Feynman integrals with all possible powers of propagators and try to reduce them, by linear relations, to a finite subset of integrals, the so-called master integrals. Up to now, there are numerous examples of reduction procedures resulting in a finite number of master integrals for various families of Feynman integrals. However, up to now it was just an empirical fact that the reduction procedure results in a finite number of irreducible integrals. It this paper we prove that the number of master integrals is always finite.

Mathematics Subject Classification (2000)

81Q30 14F10 


Feynman integrals algebraic groups D-modules 


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Copyright information

© Springer 2010

Authors and Affiliations

  1. 1.Scientific Research Computing CenterMoscow State UniversityMoscowRussia
  2. 2.Department of Higher Algebra of Moscow State UniversityMoscowRussia
  3. 3.Jacobs UniversityBremenGermany

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