Ultraviolet Stability for QED in d=3

TL;DR

This paper investigates the ultraviolet stability of quantum electrodynamics in three dimensions using a lattice-based renormalization group approach, establishing bounds in finite volume for weak coupling.

Contribution

It extends previous work by providing a rigorous ultraviolet stability bound for QED in three dimensions on a lattice, controlling the renormalization group flow at weak coupling.

Findings

Established ultraviolet stability bounds in finite volume.

Controlled the renormalization group flow for weak coupling.

Extended previous theoretical frameworks to three-dimensional QED.

Abstract

We continue the study of the ultraviolet problem for QED in d=3 using Balaban's formulation of the renormalization group. The model is defined on a fine toroidal lattice and we seek control as the lattice spacing goes to zero. Drawing on earlier papers in the series the renormalization group flow is completely controlled for weak coupling. The main result is an ultraviolet stability bound in a fixed finite volume.