The group structure of dynamical transformations between quantum reference frames

Recently, it was shown that when reference frames are associated to quantum systems, the transformation laws between such need be modified take into account and dynamical features of frames. This led a relational description phase space variables system which part of. While transformations were symmetries system's Hamiltonian, question remained unanswered as whether they enjoy group structure, similar Galilei relating classical in mechanics. In this work, we identify canonical on systems comprising frames, show these close structure defined by Lie algebra, is different from usual algebra We further find elements new fact building blocks previously identified, recover. Finally, how described standard can obtained taking zero limit parameter governs additional noncommutativity introduced nature inertial transformations.