The kinematical Hilbert space of Loop Quantum Gravity from BF theories

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

Revised Conditions for MRI due to Isorotation Theorem

We re-analyze the physical conditions for Magneto-rotational Instability (MRI) within a steady axisymmetric stratified disk of plasma, in order to account for the so-called isorotation theory (the spatial profile of differential angular velocity depends on the magnetic flux surface). We develop the study of linear stability around an astrophysical background configuration, following the original derivation in \cite{Ba:1995}, but implementing the isorotation condition as the orthogonality between the background magnetic field and the angular velocity gradient. We demonstrate that a dependence on the background magnetic field direction is restored in the dispersion relation and, hence, the emergence of MRI is also influenced by field orientation.Comment: 9 pages, 2 figures, accepted for publication in Physics Letters