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.