The Liouville field theory zero-mode problem
200423 pages
Published in:
- Theor.Math.Phys. 139 (2004) 654-671,
- Teor.Mat.Fiz. 139 (2004) 245-267
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Abstract: (Springer)
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(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.- conformal field theory
- Liouville theory
- Hamiltonian reduction
- Liouville particle dynamics
- zero modes
- half-plane quantization
- field theory: conformal
- dimension: 2
- field theory: Liouville
- zero mode
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