DELICACIES OF MASS PERTURBATION IN THE SCHWINGER MODEL ON A CIRCLE

The Hilbert bundle for the massless fermions of the Schwinger model on a circle, over the space of gauge field configurations, is topologica lly nontrivial (twisted). The corresponding bundle for massive fermion s is topologically trivial (periodic). Since the structure of the ferm ionic Hilbert bundle changes discontinuously the possibility of pertur bing in the mass is thrown into doubt. In this paper we show that a di rect application of the antiadiabatic theorem of Low allows the struct ure of the massless theory to be dynamically preserved in the strong c oupling limit, e/m >> 1. This justifies the use of perturbation theory in the bosonized version of the model, in this limit.