The uncertainty of fluxes
type: Item
instance of: scholarly article
title: The uncertainty of fluxes
zbMATH Open document ID: 1126.81045
author: Daniel S. Freed
author: G. W. Moore
author: Graeme Segal
published in: Communications in Mathematical Physics
publication date: 2007-10-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-th/0605198
review text: The development of quantum electrodynamics by Dirac (1927) produced rules for the equal time commutator of the electric and magnetic fields as operators while the components of the electric field commute among themselves, and so do the components of the magnetic field. Subsequently, Bohr and Rosenfeld (1933) started discussing thought experiments to verify that electric and magnetic fields cannot be measured simultaneously with arbitrary precision. The present article extends this discussion in a purely mathematical manner to a situation where the underlying Euclidean space is replaced by a compact oriented Riemannian 3-manifold. The fields under discussion are still free, i.e.\ electric and magnetic currents are set to zero. The uncertainty discovered this way reflects torsion. Not only does the argument apply to abelian gauge fields in general, but also to the so-called \(B\)-field and the Ramond-Ramond field in 10-dimensional superstring theory. Here the quantization is expressed in terms of topological \(K\)-theory and it is shown here that the Hilbert space of states is graded by \(K\)-theory modulo torsion, hence is \(\mathbb Z/2\mathbb Z\)-graded.
Mathematics Subject Classification ID: 81T20
Mathematics Subject Classification ID: 81T70
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 58J90
Mathematics Subject Classification ID: 19M05
Mathematics Subject Classification ID: 81V10
Mathematics Subject Classification ID: 81Q70
zbMATH DE Number: 5204073
zbMATH Keywords: Maxwell theory
zbMATH Keywords: quantisation
zbMATH Keywords: curved space
zbMATH Keywords: uncertainty relation
reviewed by: Gert Roepstorff
MaRDI profile type: Publication
OpenAlex ID: W2085541615
arXiv ID: hep-th/0605198
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DOI: 10.1007/S00220-006-0181-3
description: scientific article