Skip to main content

Part of the book series: Texts & Monographs in Symbolic Computation ((TEXTSMONOGR))

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 to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. K. Chetyrkin, F. Tkachov, Nucl. Phys. B 192, 159 (1981). https://doi.org/10.1016/0550-3213(81)90199-1

    Article  Google Scholar 

  2. R.N. Lee, JHEP 07, 031 (2008). https://doi.org/10.1088/1126-6708/2008/07/031

    Article  Google Scholar 

  3. J. Blümlein, Analytic integration methods in quantum field theory: an Introduction, [arXiv:2103.10652 [hep-th]], contribution to this volume

    Google Scholar 

  4. S. Laporta, Int. J. Mod. Phys. A 15, 5087 (2000). https://doi.org/10.1016/S0217-751X(00)00215-7

    MathSciNet  Google Scholar 

  5. R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [hep-ph]

    Google Scholar 

  6. M. Steinhauser, Comput. Phys. Commun. 134, 335 (2001). https://doi.org/10.1016/S0010-4655(00)00204-6

    Article  Google Scholar 

  7. A. Pikelner, Comput. Phys. Commun. 224, 282 (2018). https://doi.org/10.1016/j.cpc.2017.11.017

    Article  Google Scholar 

  8. R. Mertig, R. Scharf, Comput. Phys. Commun. 111, 265 (1998). https://doi.org/10.1016/S0010-4655(98)00042-3

    Article  Google Scholar 

  9. S.A. Larin, F.V. Tkachov, J.A.M. Vermaseren, The FORM version of MINCER, NIKHEF-H-91-18 (1991)

    Google Scholar 

  10. 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

    Article  Google Scholar 

  11. B. Ruijl, T. Ueda, J.A.M. Vermaseren, Comput. Phys. Commun. 253, 107198 (2020). https://doi.org/10.1016/j.cpc.2020.107198

    Article  MathSciNet  Google Scholar 

  12. J. Vermaseren, Some steps towards improving IBP calculations and related topics, contribution to this volume

    Google Scholar 

  13. H. Frellesvig, Top-down Decomposition: A Cut-based Approach to Integral Reductions, contribution tro this volume

    Google Scholar 

  14. A. von Manteuffel, C. Studerus, Reduze 2 - Distributed Feynman Integral Reduction, arXiv:1201.4330 [hep-ph]

    Google Scholar 

  15. C. Studerus, Comput. Phys. Commun. 181, 1293 (2010). https://doi.org/10.1016/j.cpc.2010.03.012

    Article  MathSciNet  Google Scholar 

  16. A.V. Smirnov, F.S. Chuharev, Comput. Phys. Commun. 247, 106877 (2020). https://doi.org/10.1016/j.cpc.2019.106877

    Article  Google Scholar 

  17. A.V. Smirnov, Comput. Phys. Commun. 189, 182 (2015). https://doi.org/10.1016/j.cpc.2014.11.024

    Article  Google Scholar 

  18. A.V. Smirnov, V.A. Smirnov, Comput. Phys. Commun. 184, 2820 (2013). https://doi.org/10.1016/j.cpc.2013.06.016

    Article  Google Scholar 

  19. A.V. Smirnov, JHEP 10, 107 (2008). https://doi.org/10.1088/1126-6708/2008/10/107

    Article  Google Scholar 

  20. P. Maierhöfer, J. Usovitsch, P. Uwer, Comput. Phys. Commun. 230, 99 (2018). https://doi.org/10.1016/j.cpc.2018.04.012

    Article  Google Scholar 

  21. J. Klappert, F. Lange, Comput. Phys. Commun. 247, 106951 (2020). https://doi.org/10.1016/j.cpc.2019.106951

    Article  Google Scholar 

  22. A.V. Kotikov, Differential equations and Feynman integrals, arXiv:2102.07424 [hep-ph], contribution to this volume

    Google Scholar 

  23. P. Kant, Comput. Phys. Commun. 185, 1473 (2014). https://doi.org/10.1016/j.cpc.2014.01.017

    Article  Google Scholar 

  24. J. Gluza, K. Kajda, D.A. Kosower, Phys. Rev. D 83, 045012 (2011). https://doi.org/10.1103/PhysRevD.83.045012

    Article  Google Scholar 

  25. 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]

    Google Scholar 

  26. J. Klappert, F. Lange, P. Maierhöfer, J. Usovitsch, Integral Reduction with Kira 2.0 and Finite Field Methods, arXiv:2008.06494 [hep-ph]

    Google Scholar 

  27. T. Peraro, JHEP 07, 031 (2019). https://doi.org/10.1007/JHEP07(2019)031

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Peter Marquard .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

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)

Publish with us

Policies and ethics