Exact solution of the Schwinger model with compact U(1)

The exact solution of the Schwinger model with compact gauge group U(1) is presented. The compactification is imposed ty demanding that the only survi ving true electromagnetic degree of freedom c has angular character. Not su rprisingly, this topological condition defines a version of the Schwinger m odel 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 degen erated and does not correspond to the equally spaced harmonic oscillator, b oth the electric charge and a modified gauge-invariant chiral charge are co nserved (nevertheless, the axiai-current anomaly is still present) and, fin ally, 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.