• BF theory
• inhomogeneous gauge group
• topological quantum field theory
• topological field theory
• knot
• knots
• link
• links
• knot observables
• link observables

In this thesis we study an example of topological quantum field theory, the BF theory with inhomogeneous ISU(2) gauge group. It was already known that BF theories have connected Feynman diagrams with at most one loop. Using this property, we study the generating functional of connected diagrams, finding relations with the generating functional of the Chern-Simons theory. The model is superrenormalizable and we perform explicitly the complete renormalization, showing that the beta function vanishes. This confirms the previously known scale invariance of the theory.
The definition of gauge invariant observables is an open problem. We study representations of the ISU(2) group that act on a linear space generated by eigenstates of the momentum with eigenvalues that belong a sphere of constant length radius and we define an appropriately normalized trace. We then propose as observables the Wilson loops, that is, the trace of the parallel transport along a knot, a closed, non-intersecting curve in space. We finally calculate the Wilson loops perturbatively to the second order, showing that they are ambient isotopy invariants of bands.