MG14 - Talk detail

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Abstract

Relativistic particles with momentum space described by a group manifold provide a very interesting link between gravity, quantum group symmetries and non-commutative field theories. Group valued momenta are also the main ingredient for modelling relativistic symmetry deformation at the Planck scale. The appeal of these models is that they naturally emerge in the description of a gravitating point particle in three dimensional gravity and in four dimensions they can lead to testable predictions, mainly based on their deformed energy-momentum dispersion relations. In this talk I will briefly review the basic notions of group momentum space in terms of non-local symmetry generators and how they emerge in the context of three-dimensional gravity. I will introduce a new physical interpretation of the deformed action of time translation generators on operators which characterizes these models. I will show how such action leads to a Lindblad-like evolution equation for density matrices when expanded at leading order in the Planckian deformation parameter. This evolution equation allows pure states to evolve into mixed states. This observation has potential applications for the black hole information paradox and can open new phenomenological windows for Planck scale physics.

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