The interplay between mass, volume, \theta, and <\psibar\psi> in N-flavor QED_2

TL;DR

This paper analyzes the N-flavor Schwinger model in 2D, revealing how mass, volume, and theta angle influence chiral condensates and emphasizing the non-commuting limits of massless and infinite volume/temperature.

Contribution

It provides a detailed analysis of the interplay between mass, volume, theta, and condensate behavior in N-flavor QED_2, especially for N=3, highlighting the effects of mass asymmetry.

Findings

Chiral condensate develops a cusp at θ=±π with degenerate masses.

Large mass asymmetry removes the cusp singularity.

Physical quantities depend on the combined parameter mL or m/T.

Abstract

The Schwinger model (QED_2) with N flavors of massive fermions on a circle of circumference L, or equivalently at finite temperature T, is reduced to a quantum mechanical system of N-1 degrees of freedom. With degenerate fermion masses (m) the chiral condensate develops a cusp singularity at $\theta=\pm \pi$ in the limit L -> $\infty$ or T -> 0, which is removed by a large asymmetry in the fermion masses. Physical quantities sensitively depend on the parameter mL or m/T, and the m -> 0 and L -> $\infty$ (or T -> 0) limits do not commute. A detailed analysis is given for N=3.