Geometrical meaning of braid statistics in (1+1)- and (2+1)-dimensional quantum field theory |
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Authors: | Hermann Hessling Ralf D Tscheuschner |
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Institution: | (1) II. Institut für Theoretische Physik der Universität Hamburg, D-2000 Hamburg 50, Germany;(2) I. Institut für Theoretische Physik der Universität Hamburg, D-2000 Hamburg 36, Germany |
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Abstract: | Braids naturally arise as topological objects in the discussion of statistics in quantum mechanics of indistinguishable pointlike particles moving in a (2+1)-dimensional space-time. Conversely, they also play a role as algebraic invariants in the discussion of superselection rules in (1+1)-dimensional algebraic quantum field theory. Here we show how Abelian braid statistics in (1+1) dimensions may be interpreted geometrically by introducing the concept of antiparticles, thus clarifying the connection between the two approaches. |
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