论文标题
渐近边界KZB操作员和量子Calogero-Moser旋转链
Asymptotic boundary KZB operators and quantum Calogero-Moser spin chains
论文作者
论文摘要
渐近边界KZB方程描述了边界wess-zumino-witter-witter-novikov保形场理论的相关函数退化的一致性条件。在本文的第一部分中，我们定义了与有限的中心连接的真实半圣事组G的渐近边界KZB操作员。我们使用Harish-Chandra的径向组件图的坐标版本证明了它们的主要特性。我们表明，它们的交换性受涉及经典动力学扬式方程和反射方程的耦合版本的方程式系统的控制。我们使用坐标径向组件映射来引入一类新的量子可促进系统，称为Quantum Calogero-Moser旋转链。量子calogero-moser自旋链是与G的限制根系和具有双面反射边界的一维自旋链相关的量子自旋Calogero-Moser系统的混合物。渐近边界KZB操作员为其一阶量子哈密顿人提供明确的表达式。我们还明确描述了Schrödinger操作员。
Asymptotic boundary KZB equations describe the consistency conditions of degenerations of correlation functions for boundary Wess-Zumino-Witten-Novikov conformal field theory on a cylinder. In the first part of the paper we define asymptotic boundary KZB operators for connected real semisimple Lie groups G with finite center. We prove their main properties algebraically using coordinate versions of Harish-Chandra's radial component map. We show that their commutativity is governed by a system of equations involving coupled versions of classical dynamical Yang-Baxter equations and reflection equations. We use the coordinate radial components maps to introduce a new class of quantum superintegrable systems, called quantum Calogero-Moser spin chains. A quantum Calogero-Moser spin chain is a mixture of a quantum spin Calogero-Moser system associated to the restricted root system of G and an one-dimensional spin chain with two-sided reflecting boundaries. The asymptotic boundary KZB operators provide explicit expressions for its first order quantum Hamiltonians. We also explicitly describe the Schrödinger operator.
