Quantum Galilei group as quantum reference frame transformations
Apparaît dans la collection : Applications of NonCommutative Geometry to Gauge Theories, Field Theories, and Quantum Space-Time / Applications de la Géométrie Non Commutative aux Théories de Jauge, à la Théorie des Champs et aux Espaces-Temps Quantiques
Recent developments in quantum information led to a generalised notion of reference frames transformations, relevant when reference frames are associated to quantum systems. In this talk, I discuss whether such quantum reference frame transformations could realise a notion of deformed symmetries formalised as quantum group transformations. In particular, I show the correspondence between quantum reference frame transformations and transformations generated by a quantum deformation of the Galilei group with commutative time, taken at the first order in the quantum deformation parameter. This correspondence is found once the group noncommutative transformation parameters are represented on the phase space of a quantum particle, and upon setting the quantum deformation parameter to be proportional to the inverse of the mass of the particle serving as the quantum reference frame.
