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Abelian BF theory

Abstract : In this study, the abelian BF theory is considered on a closed manifold of di-mension 3. It is formulated in terms of gauge classes which appear to be Deligne-Beilinson cohomology classes. Such a formulation offers the possibility to extract the quantities mathematically relevant quantities from formal functional integrals. This way, the partition function and the expectation value of observables are computed. Those computations complete the ones performed with the abelian Chern-Simons theory and the results appear to be connected together and also with abelian Reshetikhin-Turaev and Turaev-Viro topological invariants. Two extensions of this study are also discussed. Firstly, a graphical approach is proposed to deal with the SU(N) classical Chern-Simons invariant. Secondly, a geometric interpretation of the gauge fixing procedure is presented for the abelian Chern-Simons theory in mathbb{R}^{4l+3}.
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Philippe Mathieu. Abelian BF theory. Mathematical Physics [math-ph]. Université Grenoble Alpes, 2018. English. ⟨NNT : 2018GREAY066⟩. ⟨tel-02132748⟩

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