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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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 202, No. 2, pp. 278–289, February, 2020.
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Lakehal, H., Maamache, M. Hannay Angles and Grassmannian Action—Angle Quantum States. Theor Math Phys 202, 243–251 (2020). https://doi.org/10.1134/S0040577920020075
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DOI: https://doi.org/10.1134/S0040577920020075