Abstract:
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.
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