MG12 - Talk detail
 

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Abstract

On the Removal of Time-Gauge in Loop Quantum Gravity, with and without Matter.

we perform the Hamiltonian formulation of gravity at the first order without fixing the local Lorentz frame. We demonstrate that the Gauss constraints of the Lorentz group reduce to SU(2)-Gauss constraints plus the vanishing of some momenta. This result definitively clarifies the peculiar role played by the SU(2) gauge symmetry in the phase space of gravity. Hence the Loop Quantum Gravity quantization procedure can be safely applied and no gauge condition has to be fixed for the local Lorentz frame.

On the meaning of the Immirzi field.

we investigate the possibility of treating the Immirzi parameter as a scalar field in a first-order formulation. The analysis of the phase space emphasizes the emergence of a SU(2) gauge symmetry. The super-momentum constraints coincide with the analogous ones in presence of a standard scalar field, while the form of the super-Hamiltonian is presented. It is sketched an explanation for the dynamical relaxation of the Immirzi field to a non-vanishing expectation value, thus restoring ordinary Loop Quantum Gravity.

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