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We provide a complete quantization for the Gowdy model with local rotational symmetry in vacuum. We start with a redefinition of the classical constraint algebra such that the Hamiltonian constraint has a vanishing Poisson bracket with itself. We apply a canonical quantization within loop quantum gravity and an improved dynamics scheme. We construct the exact solutions to the constraints and the physical Hilbert space, together with the physical observables. The quantization provides a physical picture without singularities. Besides, a genuine discretization of the spatial geometry emerges by means of a new quantum observable without classical analogue.

Local rotational symmetry Gowdy model in loop quantum gravity