Some combinatorial interpretations in perturbative quantum field theory
Mathematical Physics
2013-08-22 v2 Combinatorics
math.MP
Abstract
This paper will describe how combinatorial interpretations can help us understand the algebraic structure of two aspects of perturbative quantum field theory, namely analytic Dyson-Schwinger equations and periods of scalar Feynman graphs. The particular examples which will be looked at are, a better reduction to geometric series for Dyson-Schwinger equations, a subgraph which yields extra denominator reductions in scalar Feynman integrals, and an explanation of a trick of Brown and Schnetz to get one extra step in the denominator reduction of an important particular graph.
Cite
@article{arxiv.1302.0080,
title = {Some combinatorial interpretations in perturbative quantum field theory},
author = {Karen Yeats},
journal= {arXiv preprint arXiv:1302.0080},
year = {2013}
}
Comments
29 pages, written for the proceedings of the periods and motives workshop, Madrid 2012, updated with edits suggested by the referees