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

Files

hdl_130599.pdf (442.38 KB)
  (Accepted version)

Date

2021

Authors

Mickelsson, J.
Murray, M.

Editors

Advisors

Journal Title

Journal ISSN

Volume Title

Type:

Journal article

Citation

Journal of Geometry and Physics, 2021; 163:104152-104152

Statement of Responsibility

Jouko Mickelsson, Michael Murray

Conference Name

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.

School/Discipline

Dissertation Note

Provenance

Description

Access Status

Rights

© 2021 Elsevier B.V. All rights reserved.

License

Call number

Persistent link to this record