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Using a group-invariant version of the Faddeev-Popov method we explicitlyobtain the partition functions of the Self-Dual Model and Maxwell-Chern-Simonstheory. We show that their ratio coincides with the partition function ofabelian Chern-Simons theory to within a phase factor depending on thegeometrical properties of the manifold.

Erratum: Equivalence of the self-dual model and Maxwell-Chern-Simons theory on arbitrary manifolds [Phys. Rev. D59, 065019 (1999)]