# Loop quantization of the Gowdy model with local rotational symmetry

## TL;DR

This paper presents a complete loop quantum gravity quantization of the vacuum Gowdy model with local rotational symmetry, resulting in singularity-free quantum spacetimes and new geometric observables.

## Contribution

It introduces a novel redefinition of constraints, applies an improved dynamics scheme, and constructs the physical Hilbert space for the model.

## Key findings

- Quantum spacetimes are free of singularities.
- New quantum observables encode geometric discretization.
- Existing Abelianization techniques require further refinement.

## Abstract

We provide a full quantization of the vacuum Gowdy model with local rotational symmetry. We consider a redefinition of the constraints where the Hamiltonian Poisson-commutes with itself. We then apply the canonical quantization program of loop quantum gravity within an improved dynamics scheme. We identify the exact solutions of the constraints and the physical observables, and we construct the physical Hilbert space. It is remarkable that quantum spacetimes are free of singularities. New quantum observables naturally arising in the treatment partially codify the discretization of the geometry. The preliminary analysis of the asymptotic future/past of the evolution indicates that the existing Abelianization technique needs further refinement.