2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225804We present the Hamiltonian formulation of General Relativity with the Holst formulation in a generic local Lorentz frame. In particular, we outline that a Gauss constraint is inferred by a proper generalization of Ashtekar-Barbero-Immirzi connections. This feature allow to extend the Loop Quantum Gravity quantization procedure to the case in which no gauge fixing at all is performed of the Lorentz frame.8 pages, Proceedings of The 3rd Stueckelberg Workshop on Relativistic Field TheorieGeneral Relativity and Quantum Cosmologytext