Algorithm FIRE—Feynman Integral REduction

By Alexander V. Smirnov. 2008

577 citations recorded by the source corpus.

The recently developed algorithm FIRE performs the reduction of Feynman integrals to master integrals. It is based on a number of strategies, such as applying the Laporta algorithm, the s-bases algorithm, region-bases and integrating explicitly over loop momenta when possible. Currently it is being used in complicated three-loop calculations.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/20e6f38dbb189b00ccfda8fbbe32e81e5d200ec5

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In Applied Mathematics

In Atomic and Molecular Physics, and Optics

In Nuclear and High Energy Physics

Citations in the corpus

Calculation of the quark and gluon form factors to three loops in QCD (2010, methodology): “For this reduction, we used the Mathematica-based package FIRE [52] and the C++ package Reduze [53], which was developed most recently by one of us.”
FIRE5: A C++ implementation of Feynman Integral REduction (2014, methodology): “The initial version of FIRE [4, 5] was written in Wolfram Mathematica.”
Critical points and number of master integrals (2013, methodology): “Almost all publicly available programs, like FIRE [3] and Reduze [4, 5], heavily rely on the Laporta algorithm, which includes a brute-force search of the reduction rules.”
Presenting LiteRed: a tool for the Loop InTEgrals REDuction (2012, background): “Probably, the only, partly successful, attempt of this approach has been made in FIRE, where the notion of s-bases [11, 12] have been used.”
Reduze 2 - Distributed Feynman Integral Reduction (2012, methodology): “Public implementations of different reduction algorithms are available with the computer programs AIR [12], FIRE [13] and the first version of Reduze [14].”
LiteRed 1.4: a powerful tool for reduction of multiloop integrals (2013, background): “Probably, the only, partly successful, attempt to implement this approach has been made in FIRE , where the notion of s-bases [10, 11] has been used.”
Three loop analysis of the critical O (N) models in 6-ε dimensions (2014, methodology): “2) For the more complicated integrals, we use the mathematica program FIRE [41], which uses integration-by-parts (IBP) relations to turn them into simpler “master integrals”, which we then evaluate by hand.”
Reduze - Feynman integral reduction in C++ (2009, background): “Other published reduction programs are AIR [11] and FIRE [12].”