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

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dc.creatorMeusburger, C
dc.creatorSchroers, B J
dc.date2003-10-23
dc.date2004-08-27
dc.date.accessioned2026-07-07T04:16:03Z
dc.date.available2026-07-07T04:16:03Z
dc.descriptionWe 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.
dc.description35 pages, one eps figure; minor corrections
dc.identifierhttps://arxiv.org/abs/hep-th/0310218
dc.identifierhttp://arxiv.org/abs/hep-th/0310218
dc.identifierAdv.Theor.Math.Phys. 7 (2004) 1003-1043
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/52196
dc.subjectHigh Energy Physics - Theory
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectMathematical Physics
dc.titleThe quantisation of Poisson structures arising in Chern-Simons theory with gauge group $G\ltimes \mathfrak{g}^*$
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