Renormalization of QED with planar binary trees

TL;DR

This paper develops a novel algebraic framework using planar binary trees to analyze the renormalization process in QED, providing explicit recursive solutions and Hopf algebra structures for massless and massive cases.

Contribution

It introduces a new combinatorial approach to QED renormalization using planar binary trees and explicitly relates renormalized and bare expansions with algebraic structures.

Findings

Explicit recursive formulas for propagator expansions

Hopf algebra structure in massless QED

Explicit relations for massive quenched QED

Abstract

The renormalized photon and electron propagators are expanded over planar binary trees. Explicit recurrence solutions are given for the terms of these expansions. In the case of massless Quantum Electrodynamics (QED), the relation between renormalized and bare expansions is given in terms of a Hopf algebra structure. For massive quenched QED, the relation between renormalized and bare expansions is given explicitly.