Dodgson polynomial identities [article]

Marcel Golz
2018 arXiv   pre-print
Dodgson polynomials appear in Schwinger parametric Feynman integrals and are closely related to the well known Kirchhoff (or first Symanzik) polynomial. In this article a new combinatorial interpretation and a generalisation of Dodgson polynomials are provided. This leads to two new identities that relate large sums of products of Dodgson polynomials to a much simpler expression involving powers of the Kirchhoff polynomial. These identities can be applied to the parametric integrand for quantum
more » ... electrodynamics, simplifying it significantly. This is worked out here in detail on the example of superficially renormalised photon propagator Feynman graphs, but works much more generally.
arXiv:1810.06220v1 fatcat:5nsno524m5anfdbvq4knjwegji