Transformation of spin in quantum reference frames

In physical experiments, reference frames are standardly modeled through a specific choice of coordinates used to describe the systems, but they themselves not considered as such. However, any frame is system that ultimately behaves according quantum mechanics. We develop framework for rotational (i.e., spin) frames, with respect which systems spin degrees freedom described. give an explicit model such composed three coherent states angular momentum $j$ and introduce transformations between them by upgrading Euler angles occurring in classical $\text{SO}(3)$ mechanical operators acting on frames. To ensure arbitrary rotation can be applied we take limit infinitely large $j$, case angle operator possesses continuous spectrum. prove rotationally invariant Hamiltonians (such Heisenberg model) under larger group transformations. Our result development formalism non-Abelian group.