Hannay angles and Grassmannian action-angle quantum states

We show how to derive the Hannay angles of Grassmannian classical mechanics from the evolution of Grassmannian action–angle quantum states. Just as in the commutative case, this evolution defines a geometric transport, which can also be obtained from a quantum canonical transformation or a variational principle. As examples, we explicitly construct the quantum states for the classical counterparts of a first- and second-quantized $N$-level system. In the latter case, these states reduce to standard fermionic coherent states and the classical Hannay angles coincide with the quantum Berry phases.