Ultraviolet regularity for QED in d=3

TL;DR

This paper investigates the ultraviolet behavior of Quantum Electrodynamics (QED) in three dimensions using a lattice approach and renormalization group techniques, establishing control over the model as the lattice spacing diminishes.

Contribution

It introduces a nonperturbative method to control the renormalization of QED in d=3 on a lattice, demonstrating how to set bare parameters to achieve desired physical values.

Findings

Successfully controlled the renormalization group flow for QED in d=3.

Demonstrated the dependence of bare parameters on lattice spacing.

Provided a framework for ultraviolet regularity in three-dimensional QED.

Abstract

We study 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. As a first step we take a bounded field approximation and solve the renormalization problem. Namely we show that the bare energy density and the bare fermion mass can be chosen to depend on the lattice spacing, so that under the renormalization group flow they take preassigned values on unit scale. This is accomplished by a nonpertubative technique which is insensitive to whether the renormalizations are finite or infinite.