  The classical and quantum aspects of the Schwinger model on the torus are
considered. First we find explicitly all zero modes of the Dirac operator in
the topological sectors with nontrivial Chern index and is spectrum. In the
second part we determine the regularized effective action and discuss the
propagators related to it.
  Finally we calculate the gauge invariant averages of the fermion bilinears
and correlation functions of currents and densities. We show that in the
infinite volume limit the well-known result for the chiral condensate can be
obtained and the clustering property can be established.
