In this work, it is demonstrated how the kinematical Hilbert space of Loop
Quantum Gravity (LQG) can be inferred from the configuration space of BF
theories via the imposition of the Hamiltonian constraints. In particular, it
is outlined how the projection to the representations associated with
Ashtekar-Barbero connections provides the correct procedure to implement
second-class constraints and the corresponding nontrivial induced symplectic
structure. Then, the reduction to SU(2) invariant intertwiners is analyzed and
the properties of LQG states under Lorentz transformations is discussed.Comment: 13 page