Geodesic
The Liouville Field Theory Zero-Mode Problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 2, pp. 245-267 Cet article a éte moissonné depuis la source Math-Net.Ru

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We quantize the canonical free-field zero modes $p$, $q$ on the half-plane $p>0$ for both Liouville field theory and its reduced Liouville particle dynamics. We describe the particle dynamics in detail, calculate one-point functions of particle vertex operators, deduce their zero-mode realization on the half-plane, and prove that the particle vertex operators act self-adjointly on the Hilbert space $L^2(\mathbb{R}_+)$ because of symmetries generated by the $S$-matrix. Similarly, we obtain the self-adjointness of the corresponding Liouville field theory vertex operator in the zero-mode sector by applying the Liouville reflection amplitude, which is derived by the operator method.
Keywords: conformal field theory, Liouville theory, Hamiltonian reduction, half-plane quantization.
Mots-clés : Liouville particle dynamics, zero modes 
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G. P. Jorjadze; G. Weigt. The Liouville Field Theory Zero-Mode Problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 2, pp. 245-267. http://geodesic.mathdoc.fr/item/TMF_2004_139_2_a4/

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