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Boundary Liouville Theory: Hamiltonian Description and Quantization
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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Boundary Liouville Theory: Hamiltonian Description and Quantization
Інший ID:
2000 Mathematics Subject Classification: 37K05; 37K30; 81T30; 81T40
Посилання:
Boundary Liouville Theory: Hamiltonian Description and Quantization / H. Dorn, G. Jorjadze // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 19 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the O’Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 22–24, 2006, Budapest, Hungary). We thank Cosmas Zachos for helpful discussions. G.J. is grateful to the organizers of “The O’Raifeartaigh Symposium” for the invitation. He thanks Humboldt University, AEI Golm, ICTP Trieste and ANL Argonne for hospitality, where a main part of his work was done. His research was supported by grants from the DFG (436 GEO 17/3/06) and GRDF (GEP1-3327-TB-03). H.D. was supported in part by DFG with the grant DO 447-3/3.
Дата:
2007
Переглядів:
487
Завантажень:
224
Анотація:
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.
