Infrared behaviour of massless QED in space-time dimensions 2 < d < 4

TL;DR

This paper demonstrates that infrared divergences in massless QED in 2+1 dimensions can be eliminated at all orders using a non-local gauge, leading to a conformal invariant theory across dimensions 2<d<4.

Contribution

It introduces a gauge choice that removes infrared divergences at all orders in 1/N, ensuring the infrared behavior remains unchanged by higher order corrections.

Findings

Infrared divergences are removable at all orders in 1/N.

The analysis provides a scheme for the Amati-Testa model.

Results yield a non-trivial conformal invariant field theory for 2<d<4.

Abstract

We show that the logarithmic infrared divergences in electron self-energy and vertex function of massless QED in 2+1 dimensions can be removed at all orders of 1/N by an appropriate choice of a non-local gauge. Thus the infrared behaviour given by the leading order in 1/N is not modified by higher order corrections. Our analysis gives a computational scheme for the Amati-Testa model, resulting in a non-trivial conformal invariant field theory for all space-time dimensions 2 < d < 4.