Fermions in the chiral Schwinger model

We derive an operator solution for the fermion in the chiral Schwinger model with a Wess-Zumino term and study the quantum structure of the model in a manifestly covariant operator formalism. The U(1${)}_{\mathrm{L}}$ gauge symmetry restored by the inclusion of the Wess-Zumino term gets spontaneously broken and the gauge field becomes massive. The left-handed fermion is found to be confined. The right-handed fermion, on the other hand, remains a massless free field in spite of the fact that the left- and right-handed sectors of the model are coupled through the anomaly. This massless fermion is interpreted as the Nambu-Goldstone mode associated with the spontaneous breakdown of the global U(1${)}_{\mathrm{R}}$ symmetry.