The corolla polynomial: a graph polynomial on half-edges

TL;DR

The paper reviews the corolla polynomial, a third graph polynomial based on half-edges, which aids in transitioning from scalar to gauge theory amplitudes, building on the Symanzik polynomials.

Contribution

It introduces and discusses the corolla polynomial, a novel graph polynomial based on half-edges, and its role in gauge theory amplitude calculations.

Findings

The corolla polynomial simplifies gauge theory amplitude computations.

Graph homology is instrumental in constructing the corolla polynomial.

The corolla polynomial extends the utility of graph polynomials in quantum field theory.

Abstract

The study of Feynman rules is much facilitated by the two Symanzik polynomials, homogeneous polynomials based on edge variables for a given Feynman graph. We review here the role of a recently discovered third graph polynomial based on half-edges which facilitates the transition from scalar to gauge theory amplitudes: the corolla polynomial. We review in particular the use of graph homology in the construction of this polynomial.