Enumerative Methods in Quantum Electrodynamics

TL;DR

This paper introduces a combinatorial approach using chord diagrams to analyze observables in QED-type theories, simplifying asymptotic analysis and revealing new correlations between diagram counts in different quantum field theories.

Contribution

It presents a novel combinatorial representation for QED observables that bypasses traditional singularity analysis methods.

Findings

Chord diagrams effectively model QED observables.

The new method simplifies asymptotic behavior studies.

Uncovered correlation between Feynman diagrams in Yukawa theory and quenched QED.

Abstract

We show that observables in QED-type theories can be realized in terms of a combinatorial structure called chord diagrams. One advantage of this combinatorial representation is that it simplifies the study of the asymptotic behavior of corresponding Green functions. Particularly, using the new representation, there is no need to use the standard approach of singularity analysis. This relation also reveals the unexplained correlation between the number of Feynman diagrams in Yukawa theory and the diagrams in quenched QED.