Asymptotic representations of Hamiltonian diffeomorphisms and quantization

Laurent Charles, Leonid Polterovich

Research output: Contribution to journalArticlepeer-review

Abstract

We show that for a special class of geometric quantizations with “small” quantum errors, the quantum classical correspondence gives rise to an asymptotic projective unitary representation of the group of Hamiltonian diffeomorphisms. As an application, we get an obstruction to Hamiltonian actions of finitely presented groups.

Original languageEnglish
Pages (from-to)1369-1387
Number of pages19
JournalGroups, Geometry, and Dynamics
Volume16
Issue number4
DOIs
StatePublished - 2022

Funding

FundersFunder number
Israel Science Foundation1102/20

    Keywords

    • Berezin–Toeplitz quantization
    • Hamiltonian diffeomorphism
    • Symplectic manifold
    • asymptotic representation

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