Abstract The spectrum of the Laplacian operator on the positive theta line bundle over the quasi-torus reduces to eigenvalues π ⁢ ℓ {\pi\ell} , ℓ = 0 , 1 , … {\ell=0,1,\ldots{}} , which are called Landau levels. This paper discusses the coherent state transform for each eigenspace associated with a Landau level. We construct a unitary transform valid for each eigenspace. A concrete form of the inverse formula for the proposed transform is also obtained.

中文翻译：

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准环上朗道能级的相干状态变换

摘要 拟环面上正 theta 线丛上的拉普拉斯算子的谱简化为特征值 π ⁢ ℓ {\pi\ell} , ℓ = 0 , 1 , ... {\ell=0,1,\ldots{} } ，称为朗道水平。本文讨论了与朗道水平相关的每个特征空间的相干状态变换。我们构造了一个对每个特征空间都有效的酉变换。还获得了所提出的变换的逆公式的具体形式。