Mb. Paranjape, DELICACIES OF MASS PERTURBATION IN THE SCHWINGER MODEL ON A CIRCLE, Physical review. D. Particles and fields, 48(10), 1993, pp. 4946-4951
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.