2019/03/07 by Richard J. Szabo · 8 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algorithm #Canonical quantization #Computer science #Creation and annihilation operators #Geometric quantization #Homotopy and Cohomology in Algebraic Topology #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Poisson distribution #Poisson manifold #Pure mathematics #Quantization (signal processing) #Quantum #Quantum gravity #Quantum mechanics #Second quantization #String theory #Symplectic geometry #Theoretical physics #hep-th #math-ph #math.DG #math.MP #math.QA #math.SG
paper · pdf · doi:10.1002/prop.201910022
published in Fortschritte der Physik 67(8-9) (Wiley) · 13 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018
arxiv created 2019/03/07 · openalex publication_date 2019/06/14 · arxiv updated 2021/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.