Square integrability of group representations on homogeneous spaces. II : Coherent and quasi-coherent states. The case of the Poincaré group
Square integrability of group representations on homogeneous spaces. II : Coherent and quasi-coherent states. The case of the Poincaré group
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齐次空间上群表示的平方可积性 II：相干态和准相干态 庞加莱群的情况。
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
J. Gazeau
中科院分区：
文献类型：
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作者：
Syed Twareque Ali;J. Antoine;J. Gazeau
再生三元组的概念，在系列的第一篇论文（I）中发展，被用来给出群的平方可积表示的一般定义。这个定义适用于群的齐次空间，并且概括了早期获得此类概念的尝试。除其他外，它自然导致相干态族之间的等价概念，也导致准相干态或加权相干态的概念。一般的考虑适用于具体的例子的维格纳表示的庞加莱群P+上（1，1）在一个空间和一个时间维。本文导出了一类相干态的等价族，每个相干态族对应于一个连续标架。
The concept of a reproducing triple, developed in the first paper of the series (I), is utilized to give a general definition of a square integrable representation of a group. This definition is applicable to homogeneous spaces of the group, and generalizes earlier attempts at obtaining such notions. Among others, it leads naturally to a notion of equivalence among families of coherent states, and also to the concept of quasi-coherent states, or weighted coherent states. The general considerations are applied to the specific example of the Wigner representation of the Poincare group P+up (1, 1) in one space and one time dimensions. A whole class of equivalent families of coherent states is derived, each of which corresponds to a continuous frame, in the sense of I.