Three-manifold invariant from functional integration

Journal Article · Thu Aug 15 00:00:00 EDT 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4818738· OSTI ID:22224160

Guadagnini, Enore ^[1]; Thuillier, Frank ^[2]

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1. Dipartimento di Fisica “E. Fermi” dell'Università di Pisa and INFN, Sezione di Pisa (Italy)
2. LAPTH, Université de Savoie, CNRS, Chemin de Bellevue, BP 110, F-74941 Annecy-le-Vieux cedex (France)

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.

• OSTI ID: 22224160
• Journal Information: Journal of Mathematical Physics, Vol. 54, Issue 8; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
FIELD THEORIES
PARTITION FUNCTIONS
PATH INTEGRALS
UNITARY SYMMETRY