Abstract
Following Witten, [Commun. Math. Phys. 21, 351–399 (1989)] we approach the Abelian quantum Chern–Simons (CS) gauge theory from a Feynman functional integral point of view. We show that for 3-manifolds with and without a boundary the formal functional integral definitions lead to mathematically proper expressions that agree with the results from the rigorous construction [J. Math. Phys. 39, 170–206 (1998)] of the Abelian CS topological quantum field theory via geometric quantization.
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