The quantisation of poisson structures arising in chern-simons theory with gauge group G ⋉g

C. Meusburger, B. J. Schroers

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42 Citations (Scopus)

Abstract

We quantise a Poisson structure on Hn+2g, where H is a semidirect product group of the form G × g*. This Poisson structure arises in the combinatorial description of the phase space of Chern-Simons theory with gauge group G ? g* on R × Sg,n, where Sg,n is a surface of genus g with n punctures. The quantisation of this Poisson structure is a key step in the quantisation of Chern-Simons theory with gauge group G × g*. We construct the quantum algebra and its irreducible representations and show that the quantum double D(G) of the group G arises naturally as a symmetry of the quantum algebra. © 2002 International Press.

Original languageEnglish
Pages (from-to)1003-1042
Number of pages40
JournalAdvances in Theoretical and Mathematical Physics
Volume7
Issue number6
Publication statusPublished - Dec 2003

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