Abstract
For the purposes of a combinatorial perspective on Feynman graphs , the most appropriate way to set up the graphs will not have the edges or the vertices as the fundamental bits, but rather will be based on half edges .
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
To make this precise we’d need to move into matroids. Much of what we do with Feynman graphs works very naturally with regular matroids and even some more general matroids, but that’s another story.
References
Yeats, K.: Rearranging Dyson-Schwinger equations. Mem. Am. Math. Soc. 211 (2011)
Yeats, K.A.: Growth estimates for Dyson-Schwinger equations. Ph.D. thesis, Boston University (2008)
Chapoton, F., Livernet, M.: Pre-Lie algebras and the rooted trees operad. Int. Math. Res. Not. 8(8), 395–408 (2001). arXiv:math/0002069
Kreimer, D.: Anatomy of a gauge theory. Ann. Phys. 321, 2757–2781 (2006). arXiv:hep-th/0509135v3
van Suijlekom, W.D.: Renormalization of gauge fields: a Hopf algebra approach. Commun. Math. Phys. 276, 773–798 (2007). arXiv:hep-th/0610137
Brown, F.: On the periods of some Feynman integrals. arXiv:0910.0114
Vlasev, A., Yeats, K.: A four-vertex, quadratic, spanning forest polynomial identity. Electron. J. Linear Alg. 23, 923–941 (2012). arXiv:1106.2869
Sokal, A.D.: The multivariate Tutte polynomial (alias Potts model) for graphs and matroids. In: Webb, B.S. (ed.) Surveys in Combinatorics, pp. 173–226. Cambridge (2005). arXiv:math/0503607
Cvitanović, P.: Field Theory. Nordita Lecture Notes (1983)
Zee, A.: Quantum Field Theory in a Nutshell. Princeton University Press, Princeton (2003)
Cvitanović, P., Lautrup, B., Pearson, R.B.: Number and weights of Feynman diagrams. Phys. Rev. D 18(6), 1939–1949 (1978)
Lando, S.K., Zvonkin, A.K.: Graphs on Surfaces and Their Applications. Springer, Berlin (2004)
Peskin, M.E., Schroeder, D.V.: An Introduction to Quantum Field Theory. Westview, Boulder (1995)
Cheng, T.P., Li, L.F.: Gauge Theory of Elementary Particle Physics. Oxford University Press, Oxford (1984)
Itzykson, C., Zuber, J.B.: Quantum Field Theory. McGraw-Hill (1980). Dover edition (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 The Author(s)
About this chapter
Cite this chapter
Yeats, K. (2017). Feynman Graphs. 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_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-47551-6_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-47550-9
Online ISBN: 978-3-319-47551-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)