Abstract
The present lectures give an introduction to the Doplicher-Haag-Roberts theory of superselection sectors and statistics [1,2] with special emphasis on the occurrence of braid group statistics in low-dimensional space-time [3]. We sketch the Doplicher-Roberts theorem on the relation between statistics and gauge symmetry valid for permutation group statistics [4], and terminate with two-dimensional conformal field theories providing examples of braid group statistics with particularly simple kinematics.
The DHR theory itself is an example for the effectivity of the algebraic Haag-Kastler framework [5] as an approach to the understanding of structural foundations of quantum field theory. While it proved very flexible with respect to physically motivated modifications of the basic axioms [6, 7], our presentation will be restricted to the easiest case: charges localizable within bounded regions of space-time (“particles”). The issue of statistics of a local quantum field theory may be regarded as an “invariant”, i.e. independent of the choice of a description in terms of unobservable charged fields, characterization of local algebras.
based on a review by D.Kastler, M.Mebkhout, K.-H. Rehren (ref.[10])
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© 1991 Springer-Verlag Berlin Heidelberg
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Rehren, KH. (1991). Braid Group Statistics. In: Debrus, J., Hirshfeld, A.C. (eds) Geometry and Theoretical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76353-3_4
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