Quantization of Magnetic Poisson Structures

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.

13 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018

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Cited by in corpus (6)

• Symplectic embeddings, homotopy algebras and almost Poisson gauge symmetry
• Smooth 2-Group Extensions and Symmetries of Bundle Gerbes
• T-Dualities and Doubled Geometry of the Principal Chiral Model
• A Simple Model of Double Dynamics on Lie Groups
• Topological and dynamical aspects of Jacobi sigma models
• Poisson structures on the conifold and local Calabi-Yau threefolds