Quantization of models with non-compact quantum group symmetry: Modular XXZ magnet and lattice sinh-Gordon model
Quantization of models with non-compact quantum group symmetry: Modular XXZ magnet and lattice sinh-Gordon model
复制标题
非紧量子群对称模型的量化：模块化 XXZ 磁体和晶格 sinh-Gordon 模型
DOI：
10.1088/0305-4470/39/41/s11
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
J. Teschner
中科院分区：
文献类型：
--
作者：
A. Bytsko;J. Teschner
我们定义并研究了某些具有非紧量子群对称性的可积格模型(的模偶)，包括Sinh-Gordon模型的可积格正则化和XXZ模型的非紧版本。它们的基本R-矩阵是用非紧量子双对数构造的。我们对量子群表示的选择自然确保了哈密顿量的自伴性和更高的运动积分。利用分离变量法对这些模型进行了研究。我们证明了运动积分的谱问题可以转化为确定某些有限差分方程解(Baxter方程和量子Wronskian方程)的子集的问题，该问题具有适当的解析和渐近性质。一个关键的技术工具是所谓的算子，我们给出了它的一个明确的构造。我们的结果使我们能够在连续时空中建立与Sinh-Gordon理论的相关结果和猜想的一些联系。我们的方法也从可积结构的角度揭示了质量模型和无质量模型(特别是Sinh-Gordon和Liouville理论)之间的关系。
We define and study certain integrable lattice models with non-compact quantum group symmetry (the modular double of ) including an integrable lattice regularization of the sinh-Gordon model and a non-compact version of the XXZ model. Their fundamental R-matrices are constructed in terms of the non-compact quantum dilogarithm. Our choice of the quantum group representations naturally ensures self-adjointness of the Hamiltonian and the higher integrals of motion. These models are studied with the help of the separation of variables method. We show that the spectral problem for the integrals of motion can be reformulated as the problem to determine a subset among the solutions to certain finite difference equations (Baxter equation and quantum Wronskian equation) which is characterized by suitable analytic and asymptotic properties. A key technical tool is the so-called -operator, for which we give an explicit construction. Our results allow us to establish some connections to related results and conjectures on the sinh-Gordon theory in continuous spacetime. Our approach also sheds some light on the relations between massive and massless models (in particular, the sinh-Gordon and Liouville theories) from the point of view of their integrable structures.