Feynman graph polynomials

By Christian Bogner, Stefan Weinzierl. 2010

161 citations recorded by the source corpus.

The integrand of any multiloop integral is characterized after Feynman parametrization by two polynomials. In this review we summarize the properties of these polynomials. Topics covered in this paper include among others: spanning trees and spanning forests, the all-minors matrix-tree theorem, recursion relations due to contraction and deletion of edges, Dodgson's identity and matroids.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/327d58af748714c2fa4b7db7f3ebabaae94e3696

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In Discrete Mathematics and Combinatorics

1. Erik Panzer
2. Costas G. Papadopoulos
3. Hjalte Frellesvig
4. A. Manteuffel

In Mathematical Physics

1. Robert M. Schabinger
2. Erik Panzer
3. A. Manteuffel

In Nuclear and High Energy Physics

1. Erik Panzer
2. A. Manteuffel
3. Hjalte Frellesvig
4. Robert M. Schabinger
5. C. Studerus
6. Costas G. Papadopoulos
7. Gudrun Heinrich
8. P. Maierhöfer

Citations in the corpus

• Reduze 2 - Distributed Feynman Integral Reduction (2012, background): “of edge variables exactly if their matroids are isomorphic, see [28] and references therein.”
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals (2014, background): “The two graph polynomials ψ and φ are for example defined in [52], the δ-distribution freezes an arbitrary αeN .”
• Feynman integrals and hyperlogarithms (2015, background): “This formula is also known as the all-minors matrix-tree theorem [35].”
• Cuts of Feynman Integrals in Baikov representation (2017, background): “The overall most successful one, is based on expressing the FI in terms of an integral representation over Feynman parameters, involving the two well-known Symanzik Polynomials U and F [38].”
• A quasi-finite basis for multi-loop Feynman integrals (2014, background): “where U and F are respectively the first and second Symanzik polynomials [35],”