任意子、变形振子代数和投射子
Anyons, Deformed Oscillator Algebras and Projectors
摘要：
我们提出了一种基于变形振子代数的多任意子问题的代数方法。该形式主义利用了变形海森堡代数的基础上的Calogero问题的运营商解决方案的推广。我们定义了一个多体哈密顿量和一个角动量算符，它们与统计参数nu的线性化分析有关。存在一个唯一的基态，尽管存在缺陷线，任意子的重量晶格是完全连接的应用的代数的振子。这是通过补充振荡器代数与一定的投影代数。
英文摘要：
We initiate an algebraic approach to the many-anyon problem based on deformed oscillator algebras. The formalism utilizes a generalization of the deformed Heisenberg algebras underlying the operator solution of the Calogero problem. We define a many-body Hamiltonian and an angular momentum operator which are relevant for a linearized analysis in the statistical parameter nu. There exists a unique ground state and, in spite of the presence of defect lines, the anyonic weight lattices are completely connected by the application of the oscillators of the algebra. This is achieved by supplementing the oscillator algebra with a certain projector algebra.
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