The quantisation of Poisson structures arising in Chern-Simons theory with gauge group $G\ltimes \mathfrak{g}^*$

Details The quantisation of Poisson structures arising in Chern-Simons theory with gauge group $G\ltimes \mathfrak{g}^*$ The quantisation of Poisson structures arising in Chern-Simons theory with gauge group $G\ltimes \mathfrak{g}^*$

2003-10-23

arxiv.org/abs/hep-th/0310218v2

Adv.Theor.Math.Phys. 7 (2004) 1003-1043

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, one eps figure; minor corrections

Scientific paper

We quantise a Poisson structure on H^{n+2g}, where H is a semidirect product group of the form $G\ltimes\mathfrak{g}^*$. This Poisson structure arises in the combinatorial description of the phase space of Chern-Simons theory with gauge group $G\ltimes\mathfrak{g}^*$ on $R \times S_{g,n}$, where S_{g,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 $G\ltimes\mathfrak{g}^*$. 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.

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