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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 2
A constructive Quantum Field Theoretic Approach to Chern-Simons Theory F. Nill
Int. J. Mod. Phys. B 6, No.11-12, 2159-2198 (1992)
The author reports on first results of a program he characterizes in the following way. The basic goal is toconstruct topological Chern-Simons theory as a purely kinematical quantum field theory, using as much asappropriate the algebraic concepts of local quantum fields and the Doplicher-Haag-Roberts scheme ofsuperselection sectors on the one hand and the ideas of Osterwalder-Schrader reconstruction to recover thisquantum field theory from a euclidean "functional integral" on the other hand.par Apart from an introductorysection, the paper is divided into two parts. In the first part the Weyl algebra approach to the abelianChern-Simons theory is presented which leads to the Gauss invariant of framed links (ribbons), anyon statisticsof superselection sectors and a construction of string operators as fibre isomorphisms of anyon line bundles. Inthe second part, an analogous bundle theoretical framework is presented for the non-abelian case, therebydescribing the quantum kinematics of coloured plektons. (The term "plekton" refers to the non-abeliancounterpart of "anyon".) The set of colours is specified to constitute what the author calls a "ribbon graphcategory".
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