Browsing by Author "Morales Parra, Juan Carlos"

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    Symmetries and gauge fixing of three dimensional quantum gravity
    (Heriot-Watt University, 2024-12) Morales Parra, Juan Carlos; Schroers, Professor Bernd J.
    In this thesis, we study mathematical aspects of three dimensional classical and quantum gravity. At the classical level we study the Poisson structures of gauge-fixed three dimensional Chern-Simons gravity, fully defined by classical dynamical r-matrices. We determine all the classical dynamical r-matrices associated to the Lie algebras of the local isometry groups of three dimensional spacetimes, for both the Euclidean and Lorentzian signatures and any value of the cosmological constant; highlighting these coindice with the solutions to the Classical Dynamical Yang-Baxter Equation that appear in the exchange algebra of WZNW models. At the quantum level we study two quantum group isometries of lorentzian quantum gravity: the quantum double of SL(2, R) and the quantum k-Poincaré. We prove these two Hopf algebras are twist-equivalent and examine their semiclassical counterparts.