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A Chern-Simons approach to self-dual gravity in (2+1)-dimensions and quantisation of Poisson structure

Osei, Prince K

arXiv.org, 2023-11

Ithaca: Cornell University Library, arXiv.org

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  • Título:
    A Chern-Simons approach to self-dual gravity in (2+1)-dimensions and quantisation of Poisson structure
  • Autor: Osei, Prince K
  • Assuntos: Combinatorial analysis ; Field theory (physics) ; Mathematics - Mathematical Physics ; Physics - High Energy Physics - Theory ; Physics - Mathematical Physics ; Quantum theory ; Real variables
  • É parte de: arXiv.org, 2023-11
  • Descrição: The (2+1)-dimensional analog self-dual gravity which is obtained via dimension reduction of the (3+1)-dimensional Holst action without reducing the internal gauge group is studied. A Chern-Simons formulation for this theory is constructed based on the gauge group \(SL(2,\CC)_\RR\rcross \Rsix\) and maps the 3d complex self-dual dynamical variable and connection to \(6d\) real variables which combines into a \(12d\) Cartan connection. Quantization is given by the application of the combinatorial quantisation program of Chern-Simons theory. The Poisson structure for the moduli space of flat connections on \((SL(2,\CC)_\RR\rcross \Rsix)^{n+2g}\) which emerges in the combinatorial description of the phase space on \(\RR \times \Sigma_{g,n},\) where \(\Sigma_{g,n}\) is a genus \(g\) surface with \(n\) punctures is given in terms of the classical \(r\)-matrix for the quantum double \(D(SL(2,\CC)_\RR)\) viewed as the double of a double \( D(SU(2)\dcross AN(2))\). This quantum double provides a feature for quantum symmetries of the quantum theory for the model.
  • Editor: Ithaca: Cornell University Library, arXiv.org
  • Idioma: Inglês
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