Dodgson polynomial identities

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 electrodynamics, simplifying it significantly. This makes QED Feynman integrals more accessible for both direct parametric integration via computer algebra and more abstract algebro-geometric methods.

2010 Mathematics Subject Classification

05C31, 81Q30, 81T18

Full Text (PDF format)

Received 19 December 2018

Accepted 17 April 2019

Published 6 December 2019