Inverse Landau-Khalatnikov Transformation and Infrared Critical Exponents of (2+1)-dimensional Quantum Electrodynamics

TL;DR

This paper uses an inverse Landau-Khalatnikov transformation to analyze the infrared behavior and critical exponents of (2+1)-dimensional QED, confirming previous conjectures and testing approximations through critical flavor number calculations.

Contribution

It introduces an inverse transformation approach to derive infrared properties and critical exponents in QED3, providing validation against earlier conjectures and approximations.

Findings

Infrared wave-function renormalization behavior derived in Landau gauge.

Critical exponents match earlier conjectured values.

Approximation reproduces critical flavor number for mass generation.

Abstract

By applying an inverse Landau-Khalatnikov transformation, connecting (resummed) Schwinger-Dyson treatments in non-local and Landau gauges of $QED_3$, we derive the infrared behaviour of the wave-function renormalization in the Landau gauge, and the associated critical exponents in the normal phase of the theory (no mass generation). The result agrees with the one conjectured in earlier treatments. The analysis involves an approximation, namely an expansion of the non-local gauge in powers of momenta in the infrared. This approximation is tested by reproducing the critical number of flavours necessary for dynamical mass generation in the chiral-symmetry-broken phase of $QED_3$.