The Schwinger model on $S^1$: Hamiltonian formulation, vacuum and anomaly

We present a Hamiltonian formulation of the Schwinger model on the circle in Coulomb gauge as a semi-bounded self-adjoint operator which is invariant under the modular group $\mathcal{M}=\mathbb{Z}$ of large gauge transformations. There is a nontrivial action of $\text{cm}$ on fermionic Fock space ${\text{mcH}}_0$ and its vacuum which plays a role analogous to that of the spectral flow in the formalism involving the infinite Dirac sea. The formulation allows (i) a description of the anomaly and its relation to this group action, and (ii) an explicit identification of the interacting vacuum which arises after the destabilization of the non-interacting vacuum in ${\text{mcH}}_0$.