We give a precise definition and produce a path-integral computation of the normalized partition function of the Abelian U(1) Chern-Simons field theory defined in a general closed oriented 3-manifold. We use the Deligne- Beilinson formalism, we sum over the inequivalent U(1) principal bundles over the manifold and, for each bundle, we integrate over the gauge orbits of the associated connection 1-forms. The result of the functional integration is compared with the Abelian U(1) Reshetikhin-Turaev surgery invariant.
Three-manifold invariant from functional integration
GUADAGNINI, ENORE;
2013-01-01
Abstract
We give a precise definition and produce a path-integral computation of the normalized partition function of the Abelian U(1) Chern-Simons field theory defined in a general closed oriented 3-manifold. We use the Deligne- Beilinson formalism, we sum over the inequivalent U(1) principal bundles over the manifold and, for each bundle, we integrate over the gauge orbits of the associated connection 1-forms. The result of the functional integration is compared with the Abelian U(1) Reshetikhin-Turaev surgery invariant.File in questo prodotto:
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