Abstract
We present an overview of the field of Integration-By-Parts with special emphasis on Laporta’s algorithm. We give an overview of the problems associated with Laporta’s algorithm and try to illustrate possible ways out.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
K. Chetyrkin, F. Tkachov, Nucl. Phys. B 192, 159 (1981). https://doi.org/10.1016/0550-3213(81)90199-1
R.N. Lee, JHEP 07, 031 (2008). https://doi.org/10.1088/1126-6708/2008/07/031
J. Blümlein, Analytic integration methods in quantum field theory: an Introduction, [arXiv:2103.10652 [hep-th]], contribution to this volume
S. Laporta, Int. J. Mod. Phys. A 15, 5087 (2000). https://doi.org/10.1016/S0217-751X(00)00215-7
R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [hep-ph]
M. Steinhauser, Comput. Phys. Commun. 134, 335 (2001). https://doi.org/10.1016/S0010-4655(00)00204-6
A. Pikelner, Comput. Phys. Commun. 224, 282 (2018). https://doi.org/10.1016/j.cpc.2017.11.017
R. Mertig, R. Scharf, Comput. Phys. Commun. 111, 265 (1998). https://doi.org/10.1016/S0010-4655(98)00042-3
S.A. Larin, F.V. Tkachov, J.A.M. Vermaseren, The FORM version of MINCER, NIKHEF-H-91-18 (1991)
S.G. Gorishnii, S.A. Larin, L.R. Surguladze, F.V. Tkachov, Comput. Phys. Commun. 55, 381 (1989). https://doi.org/10.1016/0010-4655(89)90134-3
B. Ruijl, T. Ueda, J.A.M. Vermaseren, Comput. Phys. Commun. 253, 107198 (2020). https://doi.org/10.1016/j.cpc.2020.107198
J. Vermaseren, Some steps towards improving IBP calculations and related topics, contribution to this volume
H. Frellesvig, Top-down Decomposition: A Cut-based Approach to Integral Reductions, contribution tro this volume
A. von Manteuffel, C. Studerus, Reduze 2 - Distributed Feynman Integral Reduction, arXiv:1201.4330 [hep-ph]
C. Studerus, Comput. Phys. Commun. 181, 1293 (2010). https://doi.org/10.1016/j.cpc.2010.03.012
A.V. Smirnov, F.S. Chuharev, Comput. Phys. Commun. 247, 106877 (2020). https://doi.org/10.1016/j.cpc.2019.106877
A.V. Smirnov, Comput. Phys. Commun. 189, 182 (2015). https://doi.org/10.1016/j.cpc.2014.11.024
A.V. Smirnov, V.A. Smirnov, Comput. Phys. Commun. 184, 2820 (2013). https://doi.org/10.1016/j.cpc.2013.06.016
A.V. Smirnov, JHEP 10, 107 (2008). https://doi.org/10.1088/1126-6708/2008/10/107
P. Maierhöfer, J. Usovitsch, P. Uwer, Comput. Phys. Commun. 230, 99 (2018). https://doi.org/10.1016/j.cpc.2018.04.012
J. Klappert, F. Lange, Comput. Phys. Commun. 247, 106951 (2020). https://doi.org/10.1016/j.cpc.2019.106951
A.V. Kotikov, Differential equations and Feynman integrals, arXiv:2102.07424 [hep-ph], contribution to this volume
P. Kant, Comput. Phys. Commun. 185, 1473 (2014). https://doi.org/10.1016/j.cpc.2014.01.017
J. Gluza, K. Kajda, D.A. Kosower, Phys. Rev. D 83, 045012 (2011). https://doi.org/10.1103/PhysRevD.83.045012
B. Agarwal, S.P. Jones, A. von Manteuffel, Two-loop helicity amplitudes for gg → ZZ with full top-quark mass effects, arXiv:2011.15113 [hep-ph]
J. Klappert, F. Lange, P. Maierhöfer, J. Usovitsch, Integral Reduction with Kira 2.0 and Finite Field Methods, arXiv:2008.06494 [hep-ph]
T. Peraro, JHEP 07, 031 (2019). https://doi.org/10.1007/JHEP07(2019)031
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Marquard, P. (2021). Integration-by-Parts: A Survey. In: Blümlein, J., Schneider, C. (eds) Anti-Differentiation and the Calculation of Feynman Amplitudes. Texts & Monographs in Symbolic Computation. Springer, Cham. https://doi.org/10.1007/978-3-030-80219-6_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-80219-6_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-80218-9
Online ISBN: 978-3-030-80219-6
eBook Packages: Computer ScienceComputer Science (R0)