### Abstract

^{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 language | English |
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Pages (from-to) | 1827-1866 |

Number of pages | 40 |

Journal | Letters in Mathematical Physics |

Volume | 109 |

Issue number | 8 |

Early online date | 21 Jan 2019 |

DOIs | |

Publication status | Published - Aug 2019 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Letters in Mathematical Physics*,

*109*(8), 1827-1866. https://doi.org/10.1007/s11005-019-01160-4

}

*Letters in Mathematical Physics*, vol. 109, no. 8, pp. 1827-1866. https://doi.org/10.1007/s11005-019-01160-4

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Geometry and 2-Hilbert space for nonassociative magnetic translations

AU - Bunk, Severin

AU - Müller, Lukas

AU - Szabo, Richard Joseph

PY - 2019/8

Y1 - 2019/8

N2 - 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.

AB - 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.

KW - Bundle gerbes

KW - Higher projective representations

KW - Magnetic monopoles

KW - Nonassociative magnetic translations

UR - http://www.scopus.com/inward/record.url?scp=85062772537&partnerID=8YFLogxK

U2 - 10.1007/s11005-019-01160-4

DO - 10.1007/s11005-019-01160-4

M3 - Article

VL - 109

SP - 1827

EP - 1866

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 8

ER -