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摘要: 通过在SL(2,R)Wess-Zumino-Novikov-Witten(缩写为WZNW)模型中加入破坏共形对称性的约束,获得了一个新的经典完全可积的二维场论体系,它把著名的sinh-Gordon方程作为其特例。这个广义sinh-Gordon体系的特点是完全可积性和可超定域化,并且描写这些特点的r矩阵是杨-Baxter方程(经典的)的一个解,它反对称,依赖于两个谱参数,但通过Loop代数的自同构变换和谱参数的重新定义后,此r矩阵仍是依赖于一个谱参数的三角型r矩阵。
Abstract: By imposing conformally broken constraints on SL(2,R) WZNW model, we obtain a new classical completely integrable system which contains the famous sinh-Gordon system as a special case. The integrability of this extended sink-Gordon system is exhibited by the existence of the Lax pair with spectral parameters. And its funda-mental .Poisson-Lie brackets can be ultralocalized, corresponding classical r-matrix depends on two spetral parameters and satisfies the classical Yang-Baxter equation. After a suitable automorphic transformation of the loop algebra on which the above Lax pair takes value, such an ultralocalized r-matrix can be classified to the so-cal-led trigonometric type of r-matrices depending essentially on one spectral parameter.