The kinematical Hilbert space of Loop Quantum Gravity from BF theories

Details The kinematical Hilbert space of Loop Quantum Gravity from BF theories The kinematical Hilbert space of Loop Quantum Gravity from BF theories

2010-12-09

arxiv.org/abs/1012.1982v3

Class. Quantum Grav. 28 (2011) 175014

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages

Scientific paper

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.

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