Dynamical variable and chiral properties of the vacuum in the Schwinger model

The Schwinger model for a system in a box is studied in the Hamiltonian formalism in the Coulomb and axial gauges. It is shown that the vacuum degeneracy in the model is a gauge artefact, and gauge-noninvariant quantities whose conservation leads to the degeneracy are specified. It is established that the dynamical variable in the model is the gauge-invariant axial charge. In the case when the vacuum is degenerate, the ground state contains a zero-mode condensate. In the limit of an infinite box, the zero mode leaves the vacuum but remains in the Hamiltonian in a separated form.