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

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.