  The exact solution of the Schwinger model with compact gauge group U(1) is
presented. The compactification is imposed by demanding that the only surviving
true electromagnetic degree of freedom has angular character. Not
surprinsingly, this topological condition defines a version of the Schwinger
model which is different from the standard one, where $c$ takes values on the
line. The main consequences are: the spectra of the zero modes is not
degenerated and does not correspond to the equally spaced harmonic oscillator,
both the electric charge and a modified gauge invariant chiral charge are
conserved (nevertheless, the axial-current anomaly is still present) and,
finally, there is no need to introduce a $\theta$-vacuum. A comparison with the
results of the standard Schwinger model is pointed out along the text.

High Energy Physics - Theory