Titlebook: Integrable Quantum Field Theories; L. Bonora,G. Mussardo,M. Martellini Book 1993 Springer Science+Business Media New York 1993 gravity.ope

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Elliptic Parametrization of the Three-State Chiral Potts Model,We establish some simple expressions for the parameters and Boltzmann weights of the three-state chiral Potts model.

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The Operator Algebra of the Discrete State Operators in 2D Gravity with Non-Vanishing Cosmological The extra discrete physical states in the 2D gravity coupled to matter have been a subject of a number of recent studies. Their existance had been observed in the matrix model approach [1] for . = 1 theory, and they have been defined in the continuum theory and further analyzed in [2, 3, 4, 5, 6, 7], for more general class of theories.

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The Partition Function of 2D String Theory,We derive a compact and explicit expression for the generating functional of all correlation functions of tachyon operators in 2D string theory. This expression makes manifest relations of the . = 1 system to KP flow and .. constraints. Moreover we derive a Kontsevich-Penner integral representation of this generating functional.

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,On the Quantum—Group Restriction of the Massive Thirring (Sine—Gordon) Model,. [1]. In integrable statistical lattice models the local Boltzmann weights are solutions of YB, or star—triangle, relations [2]. Similarly, the two—body .—matrix of integrable Quantum Field Theories satisfies the YB factorizability equations. In both cases, the YB relations are at the basis of the

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Hidden Goemetrical Structures in Integrabel Models,systems and the Coxeter element. An informal review of some of this material is given, mentioning also a couple of other contexts — the Pasquier models, and the simply-laced affine Toda field theories — where similar structures are encountered. The relevance of twisted Coxeter elements is indicated,

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On the Structure of Rational Field Theory,lattice models is explored here. Specifically, one identifies the fusion rings with the chiral rings. The theories so obtained are conjectured, and largely shown, to be integrable, based on a variety of examples, and the structure of the metric in moduli space. The kink scattering theory is given by

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