Dual Graph Polynomials and a 4-face Formula

2015/08/14 by Doryn, Dmitry
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1508.03484

Abstract

We study the dual graph polynomials and the case when a Feynman graph has no triangles but has a 4-face. This leads to the proof of the duality-admissibility of all graphs up to 18 loops. As a consequence, the c₂ invariant is the same for all 4 Feynman period representations (position, momentum, parametric and dual parametric) for any physically relevant graph.

Related

• The c₂ invariant is invariant
• Graph Invariants with Connections to the Feynman Period in ϕ⁴ Theory
• Properties of c₂ invariants of Feynman graphs
• Further investigations into the graph theory of ϕ⁴-periods and the c₂ invariant
• Properties of the corolla polynomial of a 3-regular graph