Delicacies of the Mass Perturbation in the Schwinger Model on a Circle

Details Delicacies of the Mass Perturbation in the Schwinger Model on a Circle Delicacies of the Mass Perturbation in the Schwinger Model on a Circle

1993-07-07

arxiv.org/abs/hep-th/9307051v1

Phys.Rev. D48 (1993) 4946-4951

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, plain tex, UdeM-LPS-TH-93-15-

Scientific paper

10.1103/PhysRevD.48.4946

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.

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