Asymptotic representations of Hamiltonian diffeomorphisms and quantization

Laurent Charles; Leonid Polterovich

doi:https://doi.org/10.4171/GGD/696

Asymptotic representations of Hamiltonian diffeomorphisms and quantization

Laurent Charles, Leonid Polterovich

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	1369-1387
Number of pages	19
Journal	Groups, Geometry, and Dynamics
Volume	16
Issue number	4
DOIs	https://doi.org/10.4171/GGD/696
State	Published - 2022

Keywords

Berezin–Toeplitz quantization
Hamiltonian diffeomorphism
Symplectic manifold
asymptotic representation

All Science Journal Classification (ASJC) codes

Geometry and Topology
Discrete Mathematics and Combinatorics

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Cite this

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title = "Asymptotic representations of Hamiltonian diffeomorphisms and quantization",

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.",

keywords = "Berezin–Toeplitz quantization, Hamiltonian diffeomorphism, Symplectic manifold, asymptotic representation",

author = "Laurent Charles and Leonid Polterovich",

note = "Publisher Copyright: {\textcopyright} 2022 European Mathematical Society Published by EMS Press.",

year = "2022",

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language = "الإنجليزيّة",

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AU - Charles, Laurent

AU - Polterovich, Leonid

PY - 2022

Y1 - 2022

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AB - 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.

KW - Berezin–Toeplitz quantization

KW - Hamiltonian diffeomorphism

KW - Symplectic manifold

KW - asymptotic representation

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DO - https://doi.org/10.4171/GGD/696

M3 - مقالة

SN - 1661-7207

VL - 16

SP - 1369

EP - 1387

JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

IS - 4

ER -

Asymptotic representations of Hamiltonian diffeomorphisms and quantization

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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