Dynamic variable and chiral properties of vacuum in the Schwinger model

The Schwinger model is studied in the Hamiltonian formalism for the system in a box in the Coulomb and axial gauges. It is shown that the vacuum degeneracy in the model is a gauge artifact. The gauge dependent quantities whose conservation gives rise to the degeneracy are pointed out. It is established, the dynamical varaible in the model is a guage invariant axial charge. When the vacuum degeneracy takes place, the ground state contains a zero-mode condensate. In the infinite box limit the zero-mode disappears from the vacuum but it is still present in the Hamiltonian in an isolated form