Non-associative magnetic translations from parallel transport in projective Hilbert bundles

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dc.contributor.authorMickelsson, J.
dc.contributor.authorMurray, M.
dc.date.issued2021
dc.description.abstractThe 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.
dc.description.statementofresponsibilityJouko Mickelsson, Michael Murray
dc.identifier.citationJournal of Geometry and Physics, 2021; 163:104152-104152
dc.identifier.doi10.1016/j.geomphys.2021.104152
dc.identifier.issn0393-0440
dc.identifier.issn1879-1662
dc.identifier.orcidMurray, M. [0000-0003-3713-9623]
dc.identifier.urihttp://hdl.handle.net/2440/130599
dc.language.isoen
dc.publisherElsevier
dc.rights© 2021 Elsevier B.V. All rights reserved.
dc.source.urihttps://doi.org/10.1016/j.geomphys.2021.104152
dc.subjectQuantum field theory; Hilbert bundles; magnetic translations; Non-associativity; Gerbe
dc.titleNon-associative magnetic translations from parallel transport in projective Hilbert bundles
dc.typeJournal article
pubs.publication-statusPublished

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