On the mass spectrum of noncommutative Schwinger model in Euclidean $\mathbb{R}^{2}$ space

TL;DR

This paper investigates the mass spectrum of noncommutative QED in two-dimensional Euclidean space, finding it reduces to a single meson similar to the commutative Schwinger model, through both perturbative and nonperturbative methods.

Contribution

It provides the first derivation of the noncommutative QED mass spectrum in 2D using both perturbative and nonperturbative techniques, showing its equivalence to the commutative case.

Findings

Mass spectrum reduces to a single meson with mass g/√π

Perturbative and nonperturbative approaches agree on the spectrum

Spectrum matches the commutative Schwinger model result

Abstract

The mass spectrum of the noncommutative QED in two-dimensional Euclidean $\mathbb{R}^{2}$ space is derived first in a perturbative approach at one-loop level and then in a nonperturbative approach using the equivalent bosonized noncommutative effective action. It turns out that the mass spectrum of noncommutative QED in two dimensions reduces to a single non-interacting meson with mass $M_{\gamma}=\frac{g}{\sqrt{\pi}}$, as in commutative Schwinger model.