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By using the Atiyah-Singer theorem through some similarities with theinstanton and the anti-instanton moduli spaces, the dimension of the modulispace for two and four-dimensional BF theories valued in different backgroundmanifolds and gauge groups scenarios is determined. Additionally, we developDirac's canonical analysis for a four-dimensional modified BF theory, whichreproduces the topological YM theory. This framework will allow us tounderstand the local symmetries, the constraints, the extended Hamiltonian andthe extended action of the theory.

Dimension of the moduli space and Hamiltonian analysis of BF field theories