Abstract. The quantum discrete Liouville model in the strongly coupled regime, 1 < c < 25, is formulated as a well defined quantum mechanical problem with unitary evolution operator. The theory is selfdual: there are two exponential fields related by Hermitean conjugation, satisfying two discrete quantum Liouville equations, and living in mutually commuting subalgebras of the quantum algebra of observables.
Abstract.The hamiltonian formalism is developed for the Sine-Gordon model on the spacetime light-like lattice, first introduced by Hirota. The evolution operator is explicitely constructed in the quantum variant of the model, the integrability of corresponding classical finite-dimensional system is established.
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