二维Hannay-Berry模型
The Two Dimensional Hannay-Berry Model
摘要：
本文的主要目的是在二维辛环面上构造量子力学的Hannay-Berry模型。我们构造了函数代数和线性辛群$\G =$ SL $_2 (\Z)$的同时量子化。通过$\G$在Rieffel量子环面$\Ad$不可约表示的等价类集合上的作用，得到了量子化.对于$\h \in \Q$，此操作具有唯一的固定点。这给出了一个规范的投射等变量子化。存在一个Hilbert空间，$\G$和$\Ad$在该空间上作用是等变的。结合$\G$的每一个射影表示都可以提升为线性表示的事实，我们还得到了线性等变量化。
英文摘要：
The main goal of this paper is to construct the Hannay-Berry model of quantum mechanics, on a two dimensional symplectic torus. We construct a simultaneous quantization of the algebra of functions and the linear symplectic group $\G =$ SL$_2 (\Z)$. We obtain the quantization via an action of $\G$ on the set of equivalence classes of irreducible representations of Rieffel`s quantum torus $\Ad$. For $\h \in \Q$ this action has a unique fixed point. This gives a canonical projective equivariant quantization. There exists a Hilbert space on which both $\G$ and $\Ad$ act equivariantly. Combined with the fact that every projective representation of $\G$ can be lifted to a linear representation, we also obtain linear equivariant quantization.
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