Berezin-Toeplitz quantization, hyperk\"ahler manifolds, and multisymplectic manifolds

TL;DR

This paper explores Berezin-Toeplitz quantization applied to hyperk"ahler and multisymplectic manifolds, demonstrating its effectiveness and semiclassical properties in these complex geometric settings.

Contribution

It introduces a method for quantizing hyperk"ahler and multisymplectic manifolds using Berezin-Toeplitz techniques, extending quantization to new geometric contexts.

Findings

Quantization has reasonable semiclassical properties.

Applicable to compact hyperk"ahler manifolds with 3-plectic forms.

Extends to compact integral K"ahler manifolds as (2n-1)-plectic manifolds.

Abstract

We suggest a way to quantize, using Berezin-Toeplitz quantization, a compact hyperkahler manifold (equipped with a natural 3-plectic form), or a compact integral Kahler manifold of complex dimension n regarded as a (2n-1)-plectic manifold. We show that quantization has reasonable semiclassical properties.