arXiv subjects
Publications and source records attributed to Y. Takimoto.
Quantum $A_N$-Toda field theory in two dimensions is investigated based on the method of quantizing canonical free field. Toda exponential operator associated with the fundamental weight $λ^1$ is constructed.
Locality is analyzed for Toda field theories by noting novel chiral description in the conventional nonchiral formalism. It is shown that the canonicity of the interacting to free field mapping described by the classical solution is automatically guaranteed by the locality. Quantum Toda theories are investigated by applying the method of free field quantization. We give Toda exponential operators associated with fundamental weight vectors as bilinear forms of chiral fields satisfying characteristic quantum exchange algebra. It is shown that the locality leads to nontrivial relations among the ${\cal R}$-matrix and the expansion coefficients of the exponential operators. The Toda exponentials are obtained for $A_2$-system by extending the algebraic method developed for Liouville theory. The canonical commutation relations and the operatorial field equations are also examined.
Quantum $A_2$-Toda field theory in two dimensions is investigated based on the method of quantizing canonical free field. Toda exponential operators associated with the fundamental weights are constructed to the fourth order in the cosmological constant. This leads us to a conjecture for the exact operator solution.
Correlation functions of Toda field vertices are investigated by applying the method of integrating zero-mode developed for Liouville theory. We generalize the relations among the zero-, two- and three-point couplings known in Liouville case to arbitrary Toda theories. Two- and three-point functions of Toda vertices associated with the simple roots are obtained.
The exact operator solution for quantum Liouville theory constructed for the generic quantum deformation parameter $q$ is extended to the case with $q$ being a root of unity. The screening charge operator becomes nilpotent in such cases and arbitrary Liouville exponentials can be obtained in finite polynomials of the screening charge.
Exact operator solution for quantum Liouville theory is investigated based on the canonical free field. Locality, the field equation and the canonical commutation relations are examined based on the exchange algebra hidden in the theory. The exact solution proposed by Otto and Weigt is shown to be correct to all order in the cosmological constant.