Skip to main content
SpringerLink
Log in
Book cover

A Combinatorial Perspective on Quantum Field Theory pp 113–115Cite as

Combinatorial Aspects of Some Integration Algorithms

  • Chapter
  • First Online:

  • 1374 Accesses

Part of the book series: SpringerBriefs in Mathematical Physics ((BRIEFSMAPHY,volume 15))

Abstract

The art of computing Feynman integrals has always involved graph theory in the sense that the specific structure of each Feynman graph really matters. Feynman integration is very hard so quantum field theorists have become very skilled at extracting every bit of information they can from the structure of the graphs as well as having many more analytic tricks.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   64.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

References

  1. Brown, F., Yeats, K.: Spanning forest polynomials and the transcendental weight of Feynman graphs. Commun. Math. Phys. 301(2), 357–382 (2011). arXiv:0910.5429

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Bogner, C.: MPL—a program for computations with iterated integrals on moduli spaces of curves of genus zero. Comput. Phys. Commun. 203, 339–353 (2016)

    Article  ADS  Google Scholar 

  3. Panzer, E.: Feynman integrals via hyperlogarithms. In the proceedings listed as [1]. arXiv:1407.0074

  4. Panzer, E.: On hyperlogarithms and Feynman integrals with divergences and many scales. J. High Energ. Phys. 2014, 71 (2014). arXiv:1401.4361

    Article  Google Scholar 

  5. Panzer, E.: Feynman integrals and hyperlogarithms. Ph.D. thesis, Humboldt-Universität zu Berlin (2015). arXiv:1506.07243

  6. Schnetz, O.: Graphical functions and single-valued multiple polylogarithms. Commun. Number Theory Phys. 8(4), 589–675 (2014). arXiv:1302.6445

    Article  MathSciNet  MATH  Google Scholar 

  7. Broadhurst, D., Kreimer, D.: Knots and numbers in \(\phi ^4\) theory to 7 loops and beyond. Int. J. Mod. Phys. C6(519–524) (1995). arXiv:hep-ph/9504352

  8. Brown, F., Schnetz, O.: Single-valued multiple polylogarithms and a proof of the zig-zag conjecture. J. Number Theor. 148, 478–506 (2015). arXiv:1208.1890

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada

    Karen Yeats

  2. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada

    Karen Yeats

Authors
  1. Karen Yeats
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Karen Yeats .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 The Author(s)

About this chapter

Cite this chapter

Yeats, K. (2017). Combinatorial Aspects of Some Integration Algorithms. In: A Combinatorial Perspective on Quantum Field Theory. SpringerBriefs in Mathematical Physics, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-319-47551-6_16

Download citation

Publish with us

Policies and ethics

Search

Navigation