Wigner–Weyl isomorphism for quantum mechanics on Lie groups
Wigner–Weyl isomorphism for quantum mechanics on Lie groups
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李群上量子力学的维格纳-韦尔同构
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
R. Simon
中科院分区：
文献类型：
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作者：
N. Mukunda;G. Marmo;A. Zampini;S. Chaturvedi;R. Simon
详细地研究了紧致单李群G上量子力学的Wigner-Weyl同构。几个功能出现，没有同行在熟悉的笛卡尔的情况下。其中值得注意的是半量子化相空间的概念，在这种结构上，算子的外尔符号被自然地定义，并且形象地说，位于经典相空间T*G和G上平方可积函数的希尔伯特空间之间。给出了外尔符号的星星积的一般表达式，并在角-角动量情况下明确地计算出来。
The Wigner–Weyl isomorphism for quantum mechanics on a compact simple Lie group G is developed in detail. Several features are shown to arise which have no counterparts in the familiar Cartesian case. Notable among these is the notion of a semiquantized phase space, a structure on which the Weyl symbols of operators turn out to be naturally defined and, figuratively speaking, located midway between the classical phase space T*G and the Hilbert space of square integrable functions on G. General expressions for the star product for Weyl symbols are presented and explicitly worked out for the angle-angular momentum case.