The kinematical Hilbert space of loop quantum gravity from BF theories

Francesco Cianfrani (1)

1 Dipartimento di Fisica

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.

Mots clés: Physical Sciences

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Francesco Cianfrani. The kinematical Hilbert space of loop quantum gravity from BF theories. Classical and Quantum Gravity, 2011, 28 (17), pp.175014. ⟨10.1088/0264-9381/28/17/175014⟩. ⟨hal-00728909⟩