Subnormal operators regarded as generalized observables and compound-system-type normal extension related to (1,1)
Subnormal operators regarded as generalized observables and compound-system-type normal extension related to (1,1)
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次正规算子被视为广义可观测量和与 (1,1) 相关的复合系统型正规扩展
DOI：
10.1088/0305-4470/33/43/309
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
F. Sakaguchi
中科院分区：
文献类型：
--
作者：
Masahito Hayashi;F. Sakaguchi
在这篇文章中，次正规算子，不一定是有界的，被讨论为广义可观测。为了描述其度量的输出数据的概率分布信息及其实现框架，我们引入了复合系统型正规扩张的新概念，并从代数(1，1)的不可约么正表示出发，导出了次正规算子的复合系统型正规扩张。从这个观点出发，将压缩态刻画为算符的本征向量，并证明了多粒子系统中的压缩态是这些次正规算符在某种表象下的伴随的本征向量。仿射相干态也是在同样的背景下讨论的。
In this paper, subnormal operators, not necessarily bounded, are discussed as generalized observables. In order to describe not only the information about the probability distribution of the output data of their measurement but also the framework of their implementations, we introduce a new concept of a compound-system-type normal extension, and we derive the compound-system-type normal extension of a subnormal operator, which is defined from an irreducible unitary representation of the algebra (1,1). The squeezed states are characterized as the eigenvectors of an operator from this viewpoint, and the squeezed states in multi-particle systems are shown to be the eigenvectors of the adjoints of these subnormal operators under a representation. The affine coherent states are discussed in the same context, as well.