Quantization of Coset space σ-Models coupled to Two-dimensional Gravity
نویسنده
چکیده
The mathematical framework for an exact quantization of the two-dimensional coset space σmodels coupled to dilaton gravity, that arise from dimensional reduction of gravity and supergravity theories, is presented. This work extends the previous results of [45]. The two-time Hamiltonian formulation is obtained, which describes the complete phase space of the model in the whole isomonodromic sector. The Dirac brackets arising from the coset constraints are calculated. Their quantization allows to relate exact solutions of the corresponding Wheeler-DeWitt equations to solutions of a modified (Coset) Knizhnik-Zamolodchikov system. On the classical level, a set of observables is identified, that is complete for essential sectors of the theory. Quantum counterparts of these observables and their algebraic structure are investigated. Their status in alternative quantization procedures is discussed, employing the link with Hamiltonian Chern-Simons theory. ∗On leave of absence from Steklov Mathematical Institute, Fontanka, 27, St.Petersburg 191011 Russia 1
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