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|Title:||Non-associative magnetic translations from parallel transport in projective Hilbert bundles|
|Citation:||Journal of Geometry and Physics, 2021; 163:104152-104152|
|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.|
|Appears in Collections:||Aurora harvest 8|
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