Topological BF Theories in 3 and 4 Dimensions

Abstract

In this paper we discuss topological BF theories in 3 and 4 dimensions. Observables are associated to ordinary knots and links (in 3 dimensions) and to 2-knots (in 4 dimensions). The vacuum expectation values of such observables give a wide range of invariants. Here we consider mainly the 3-dimensional case, where these invariants include Alexander polynomials, HOMFLY polynomials and Kontsevich integrals.

25 pages, latex, no figures. Transmission problems have been solved

References in corpus (4)

• Weaving a classical geometry with quantum threads
• The Donaldson-Witten Invariants in Pure QCD with Order and Disorder 't Hooft-like Operators
• Three-dimensional BF Theories and the Alexander-Conway Invariant of Knots
• On a geometric derivation of Witten's identity for Chern-Simons theory

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