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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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