Geometry and 2-Hilbert space for nonassociative magnetic translations

Severin Bunk, Lukas Müller, Richard Joseph Szabo

Research output: Contribution to journalArticle

Abstract

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 Rd 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
Number of pages40
JournalLetters in Mathematical Physics
Volume109
Issue number8
Early online date21 Jan 2019
DOIs
Publication statusPublished - Aug 2019

Fingerprint

Hilbert space
Gerbe
bundles
Bundle
Quantization
geometry
Gerbes
Covariant Derivative
Poisson Structure
Geometric Approach
charged particles
strings
Strings
Curvature
curvature
Charge
operators
Closed
Operator

Keywords

  • Bundle gerbes
  • Higher projective representations
  • Magnetic monopoles
  • Nonassociative magnetic translations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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Geometry and 2-Hilbert space for nonassociative magnetic translations. / Bunk, Severin; Müller, Lukas; Szabo, Richard Joseph.

In: Letters in Mathematical Physics, Vol. 109, No. 8, 08.2019, p. 1827-1866.

Research output: Contribution to journalArticle

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