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Type: Journal article
Title: Non-associative magnetic translations from parallel transport in projective Hilbert bundles
Author: Mickelsson, J.
Murray, M.
Citation: Journal of Geometry and Physics, 2021; 163:104152-104152
Publisher: Elsevier
Issue Date: 2021
ISSN: 0393-0440
Statement of
Jouko Mickelsson, Michael Murray
Abstract: The non-associativity of translations in a quantum system with magnetic field back-ground has received renewed interest in association with topologically trivial gerbes over Rn.The non-associativity is described by a 3-cocycle of the groupRnwith values inthe unit circleS1.The gerbes over a space Mare topologically classified by the Dixmier–Douady class which is an element of H3(M,Z). However, there is a finer description interms of local differential forms of degreesd=0,1,2,3 and the case of the magnetic translations forn=3 the 2-form part is the magnetic fieldBwith non zero divergence.In this paper we study a quantum field theoretic construction in terms of n-component fermions on a circle.The nonassociativity arises when trying to lift the translation group action on the 1-particle system to the second quantized system.
Keywords: Quantum field theory; Hilbert bundles; magnetic translations; Non-associativity; Gerbe
Rights: © 2021 ElsevierB.V. All rights reserved.
DOI: 10.1016/j.geomphys.2021.104152
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