Quantum Exchange Algebra and Exact Operator Solution of $A_2$-Toda Field Theory

Details Quantum Exchange Algebra and Exact Operator Solution of $A_2$-Toda Field Theory Quantum Exchange Algebra and Exact Operator Solution of $A_2$-Toda Field Theory

1998-10-23

arxiv.org/abs/hep-th/9810189v1

Nucl.Phys. B543 (1999) 615-651

Physics

High Energy Physics

High Energy Physics - Theory

38 pages, Latex

Scientific paper

10.1016/S0550-3213(99)00017-6

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.

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