Abelian BF theory and Turaev-Viro invariant

Understand

The U(1) BF Quantum Field Theory is revisited in the light of Deligne-Beilinson Cohomology.

• We show how the U(1) Chern-Simons partition function is related to the BF one and how the latter on its turn coincides with an abelian Turaev-Viro invariant.
• Significant differences compared to the non-abelian case are highlighted.