# Quantization of Magnetic Poisson Structures

## TL;DR

This paper explores three different methods for quantizing magnetic Poisson structures, which are relevant to nonassociative quantum mechanics and string theory, comparing their benefits and limitations.

## Contribution

It provides a comprehensive comparison of deformation, symplectic, and geometric quantization approaches for magnetic Poisson structures, highlighting their respective advantages and open questions.

## Key findings

- Deformation quantization of twisted Poisson structures is effective.
- Symplectic realization offers a geometric perspective.
- Geometric quantization via bundle gerbes is promising for nonassociative cases.

## Abstract

We describe three perspectives on higher quantization, using the example of magnetic Poisson structures which embody recent discussions of nonassociativity in quantum mechanics with magnetic monopoles and string theory with non-geometric fluxes. We survey approaches based on deformation quantization of twisted Poisson structures, symplectic realization of almost symplectic structures, and geometric quantization using 2-Hilbert spaces of sections of suitable bundle gerbes. We compare and contrast these perspectives, describing their advantages and shortcomings in each case, and mention many open avenues for investigation.