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The number of master integrals is finite · Around

2010

The number of master integrals is finite

Smirnov, A. V., Petukhov, A. V.

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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.

Built on

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K. G. Chetyrkin and F. V. Tkachov, Nucl. Phys. B 192
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Coutinho, S.C. “A primer of algebraic D-modules”, London Math. Soc. student texts 33
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S. Laporta, Int. J. Mod. Phys. A 15
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Earlier work this paper cites.

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V. A. Smirnov, “Feynman integral calculus,” Berlin, Germany: Springer (2006) 283 p
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J. I. Kapusta and C. Gale, “Finite-Temperature Field Theory Principles and Applications,” Cambridge University Press, second edition, 2006
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C. Studerus, [0912.2546]
Cited in the paper.

Then

A. V. Smirnov and V. A. Smirnov, PoS ACAT 2007:085 [0707.3993]
2007
Later among the works it cites.
A. V. Smirnov, JHEP 0810
2008
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R. N. Lee, JHEP 0807
2008
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Y. Schröder, Nucl. Phys. Proc. Suppl. B 183
Original
2008
Later among the works it cites.

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