Abstract
Operator solution of the Schwinger-Thirring (ST) models on a cylinder is given in terms of the Abelian Higgs (AH) model with topological terms. Vacuum structure and a physical excitation of the ST model is exactly obtained. Vacua of the above two models are related with each ether in quite a nontrivial way. It is shown that the effect of instantons in the AH model corresponds to the fermion mass in the ST model. Topological field theory limits are also discussed.
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