Geometry and 2-Hilbert Space for Nonassociative Magnetic Translations

Severin Bunk, Lukas Müller, Richard J. Szabo

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We suggest a geometric approach to quantisation of the twisted Poisson structure underlying the dynamics of charged particles in fields of generic smooth distributions of magnetic charge, and dually of closed strings in locally non-geometric flux backgrounds, which naturally allows for representations of nonassociative magnetic translation operators. We show how one can use the 2-Hilbert space of sections of a bundle gerbe in a putative framework for canonical quantisation. We define a parallel transport on bundle gerbes on $\mathbb{R}^d$ and show that it naturally furnishes weak projective 2-representations of the translation group on this 2-Hilbert space. We obtain a notion of covariant derivative on a bundle gerbe and a novel perspective on the fake curvature condition.
Original languageEnglish
Pages (from-to)1827-1866
JournalLetters in Mathematical Physics
Publication statusPublished - 24 Apr 2018


  • hep-th
  • math-ph
  • math.CT
  • math.MP
  • math.QA
  • quant-ph


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