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An integrable model of quantum gravity

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Nicolai,  Hermann
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Korotkin, D. A., & Nicolai, H. (1995). An integrable model of quantum gravity. Physics Letters B, 356(2-3), 211-216. doi:10.1016/0370-2693(95)00832-6.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-5B90-E
Abstract
We present a new quantization scheme for 2D gravity coupled to an SU(2) principal chiral field and a dilaton; this model represents a slightly simplified version of stationary axisymmetric quantum gravity. The analysis makes use of the separation of variables found in our previous work [D. Korotkin and H. Nicolai, Phys. Rev. Lett. 74 (1995) 1272] and is based on a two-time Hamiltonian approach. The quantum constraints are shown to reduce to a pair of compatible first order equations, with the dilaton playing the role of a “clock field”. Exact solutions of the Wheeler-DeWitt equation are constructed via the integral formula for solutions of the Knizhnik-Zamolodchikov equations.