Non-associative magnetic translations from parallel transport in projective Hilbert bundles
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(Accepted version)
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2021
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Mickelsson, J.
Murray, M.
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Journal of Geometry and Physics, 2021; 163:104152-104152
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Jouko Mickelsson, Michael Murray
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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.
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© 2021 Elsevier B.V. All rights reserved.