Mickelsson, J.Murray, M.2021-06-042021-06-042021Journal of Geometry and Physics, 2021; 163:104152-1041520393-04401879-1662http://hdl.handle.net/2440/130599The 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.en© 2021 Elsevier B.V. All rights reserved.Quantum field theory; Hilbert bundles; magnetic translations; Non-associativity; GerbeJournal article100003494510.1016/j.geomphys.2021.1041520006360848000102-s2.0-85100686735558196Murray, M. [0000-0003-3713-9623]