SIGMA 3 (2007), 012, 18 pages      hep-th/0610197      https://doi.org/10.3842/SIGMA.2007.012
Contribution to the Proceedings of the O'Raifeartaigh Symposium

Boundary Liouville Theory: Hamiltonian Description and Quantization

Harald Dorn ^a and George Jorjadze ^b
a) Institut für Physik der Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany
^b) Razmadze Mathematical Institute, M. Aleksidze 1, 0193, Tbilisi, Georgia

Received October 17, 2006, in final form December 11, 2006; Published online January 12, 2007

Abstract
The paper is devoted to the Hamiltonian treatment of classical and quantum properties of Liouville field theory on a timelike strip in 2d Minkowski space. We give a complete description of classical solutions regular in the interior of the strip and obeying constant conformally invariant conditions on both boundaries. Depending on the values of the two boundary parameters these solutions may have different monodromy properties and are related to bound or scattering states. By Bohr-Sommerfeld quantization we find the quasiclassical discrete energy spectrum for the bound states in agreement with the corresponding limit of spectral data obtained previously by conformal bootstrap methods in Euclidean space. The full quantum version of the special vertex operator e^-φ in terms of free field exponentials is constructed in the hyperbolic sector.

Key words: duality; modular symmetry; supersymmetry; quantum Hall effect.

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