Quantum self-controlling free-falling cats

In the separation of rotations from internal motions in the n-body problem, there appear some gauge fields which physically represent Coriolis effects. These fields are also present in the "falling cat" problem: at the kinematical level they map changes in the cat's shape to changes in its orientation whereas at the dynamical level they show up as gauge potentials in the Hamiltonian. Classically, the vanishing angular momentum condition allows for the orientation degrees of freedom to decouple from the internal ones and the cat's re-orientation can be accounted for at the kinematical level, partially. In the quantum case the cat's reorientation description requires to be done on dynamical grounds. In this paper we explore the quantum version of the falling cat modelled as a three body problem.