Automatic integral reduction for higher order perturbative calculations

By C. Anastasiou, A. Lazopoulos. 2004

372 citations recorded by the source corpus.

We present a program for the reduction of large systems of integrals to master integrals. The algorithm was first proposed by Laporta; in this paper, we implement it in MAPLE. We also develop two new features which keep the size of intermediate expressions relatively small throughout the calculation. The program requires modest input information from the user and can be used for generic calculations in perturbation theory.

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

View Paper: https://www.semanticscholar.org/paper/aad37756af6fd3c11c1f6fd0d08175845d562338

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In Atomic and Molecular Physics, and Optics

In Nuclear and High Energy Physics

Citations in the corpus

Integral reduction with Kira 2.0 and finite field methods (2020, background): “Several public implementations of the algorithm exist [32–35], and the implementations are continuously improved to be able to handle increasingly complicated reduction problems.”
Loop amplitudes in gauge theories: modern analytic approaches (2010, methodology): “Programs implementing the Laporta algorithm efficiently are available [126, 127, 128].”
Collider physics at the precision frontier (2020, methodology): “Public implementations of the Laporta algorithm are available in the programs Air [458], Reduze [459, 421], Fire [460–462], LiteRed [463, 464] and Kira [432, 465, 466].”
Soft triple-real radiation for Higgs production at N3LO (2013, methodology): “We implemented this algorithm in a C++ code that was developed by us specifically for this project, as well as the program AIR [87].”
Reduze - Feynman integral reduction in C++ (2009, background): “AIR is a Maple package that implements the Laporta algorithm.”
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].”
New developments in FeynCalc 9.0 (2016, methodology): “Although FeynCalc doesn’t include a general purpose tool for IBP reduction (the built-in TARCER [45] is suitable only for 2-loop self-energy type integrals), this omission can be compensated by using one of the publicly available IBP-packages (FIRE [39], LiteRED [46], Reduze [47], AIR [48]).”
FIRE5: A C++ implementation of Feynman Integral REduction (2014, background): “For other public products see [6, 7, 8, 9, 10, 11] The goal of this paper is to present the C++ version of FIRE — a powerful program for Feynman integral reduction.”