环面上的外尔表示
The Weyl representation on the torus
摘要：
我们构造的反射和平移算子的Hilbert空间对应的环面从平面上投影。这些运营商被证明具有相同的组属性作为他们的类似物在平面上。算子在反射基础上的分解对应于Weyl或中心表示，共轭于基于量化平移的弦表示。因此，任何算子在环面上的符号都是该符号在平面上的投影。群的性质使我们能够以简单的形式导出任意数目的算子的乘积律。然后利用环面上的中心和弦表示与平面上的中心和弦表示之间的类比来处理定义在环面上的Hamilton系统，并制定演化算子的路径积分表示。我们导出了它的半经典近似。
英文摘要：
We construct reflection and translation operators on the Hilbert space corresponding to the torus by projecting them from the plane. These operators are shown to have the same group properties as their analogue on the plane. The decomposition of operators in the basis of reflections corresponds to the Weyl or center representation, conjugate to the chord representation which is based on quantized translations. Thus, the symbol of any operator on the torus is derived as the projection of the symbol on the plane. The group properties allow us to derive the product law for an arbitrary number of operators in a simple form. The analogy between the center and the chord representations on the torus to those on the plane is then exploited to treat Hamiltonian systems defined on the torus and to formulate a path integral representation of the evolution operator. We derive its semiclassical approximation.
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