Asymptotic representations of Hamiltonian diffeomorphisms and quantization

TL;DR

This paper demonstrates that certain geometric quantizations with minimal quantum errors lead to asymptotic projective representations of Hamiltonian diffeomorphisms, revealing obstructions to specific group actions.

Contribution

It introduces a novel connection between geometric quantization and asymptotic group representations, providing new insights into Hamiltonian dynamics and group actions.

Findings

Asymptotic projective representations of Hamiltonian diffeomorphisms are constructed.

Obstructions to Hamiltonian actions of finitely presented groups are identified.

The results link quantum errors in quantization to classical symmetries.

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 representation of the group of Hamiltonian diffeomorphisms. As an application, we get an obstruction to Hamiltonian actions of finitely presented groups.