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The Hamiltonian formulation of the Holst action is reviewed and it isprovided a solution of second-class constraints corresponding to a genericlocal Lorentz frame. Within this scheme the form of rotation constraints can bereduced to a Gauss-like one by a proper generalization ofAshtekar-Barbero-Immirzi connections. This result emphasizes that the LoopQuantum Gravity quantization procedure can be applied when the time-gaugecondition does not stand.

Towards Loop Quantum Gravity without the time gauge