Fermion Schwinger's function for the SU(2)-Thirring model

TL;DR

This paper analyzes the two-point function of fermions in the SU(2)-Thirring model across all distance scales, combining perturbative, renormalization group, and form factor methods to understand its behavior.

Contribution

It demonstrates the application of bosonization and conformal perturbation theory in a fermionic model and validates the form factor expansion numerically for the SU(2)-Thirring model.

Findings

Short-distance asymptotics obtained via perturbation and RG analysis.

Numerical confirmation of form factor expansion validity.

Insights into fermionic two-point functions across all scales.

Abstract

We study the Euclidean two-point function of Fermi fields in the SU(2)-Thirring model on the whole distance (energy) scale. We perform perturbative and renormalization group analyses to obtain the short-distance asymptotics, and numerically evaluate the long-distance behavior by using the form factor expansion. Our results illustrate the use of bosonization and conformal perturbation theory in the renormalization group analysis of a fermionic theory, and numerically confirm the validity of the form factor expansion in the case of the SU(2)-Thirring model.