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Symmetry deformation from quantum relational observables

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Observables in (quantum) General Relativity can be constructed from (quantum) reference frame -- a physical observable is then a relation between a system of interest and the reference frame. A possible interpretation of DSR can be derived from the notion of deformed reference frame (cf Liberati-Sonego-Visser). We present a toy model and study an example of such quantum relational observables. We show how the intrinsic quantum nature of the reference frame naturally leads to a deformation of the symmetries, comforting DSR to be a good candidate to describe the QG semi-classical regime.