Combinatorial Aspects of Some Integration Algorithms
Chapter
First Online:
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.
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 ADSMathSciNetCrossRefMATHGoogle 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)ADSCrossRefGoogle 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 CrossRefGoogle 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 MathSciNetCrossRefMATHGoogle 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
Copyright information
© The Author(s) 2017