  The Hilbert bundle for the massless fermions of the Schwinger model on a
circle, over the space of gauge field configurations, is topologically
non-trivial (twisted). The corresponding bundle for massive fermions is
topologically trivial (periodic). Since the structure of the fermionic Hilbert
bundle changes discontinuously the possibility of perturbing in the mass is
thrown into doubt. In this article, we show that a direct application of the
anti-adiabatic theorem of Low, allows the structure of the massless theory to
be dynamically preserved in the strong coupling limit, ${e\over m}>>1$. This
justifies the use of perturbation theory in the bosonized version of the model,
in this limit.
