Hamiltonian analysis of \mathsf {SO}(4,1) -constrained BF theory

In this paper we discuss the canonical analysis of -constrained BF theory. The action of this theory contains topological terms appended by a term that breaks the gauge symmetry down to the Lorentz subgroup . The equations of motion of this theory turn out to be the vacuum Einstein equations. By solving the B field equations one finds that the action of this theory contains not only the standard Einstein–Cartan term but also the Holst term proportional to the inverse of the Immirzi parameter, as well as a combination of topological invariants. We show that the structure of the constraints of an -constrained BF theory is exactly that of gravity in the Holst formulation. We also briefly discuss the quantization of the theory.