dorsal/arxiv
View SchemaSubnormal operators regarded as generalized observables and compound-system-type normal extension related to su(1,1)
| Authors | Masahito Hayashi, Fuminori Sakaguchi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0003079 |
| URL | https://arxiv.org/abs/quant-ph/0003079 |
| DOI | 10.1088/0305-4470/33/43/309 |
| Journal | Journal of Physics A: Mathematical and General, Vol.33, No.43, pp.7793-7820 (2000) |
Abstract
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 a framework of their implementations, we introduce a new concept 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 su(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.
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"abstract": "In this paper, subnormal operators, not necessarily bounded, are discussed as\ngeneralized observables. In order to describe not only the information about\nthe probability distribution of the output data of their measurement but also a\nframework of their implementations, we introduce a new concept\ncompound-system-type normal extension, and we derive the compound-system-type\nnormal extension of a subnormal operator, which is defined from an irreducible\nunitary representation of the algebra su(1,1). The squeezed states are\ncharacterized as the eigenvectors of an operator from this viewpoint, and the\nsqueezed states in multi-particle systems are shown to be the eigenvectors of\nthe adjoints of these subnormal operators under a representation. The affine\ncoherent states are discussed in the same context, as well.",
"arxiv_id": "quant-ph/0003079",
"authors": [
"Masahito Hayashi",
"Fuminori Sakaguchi"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/33/43/309",
"journal_ref": "Journal of Physics A: Mathematical and General, Vol.33, No.43,\n pp.7793-7820 (2000)",
"title": "Subnormal operators regarded as generalized observables and compound-system-type normal extension related to su(1,1)",
"url": "https://arxiv.org/abs/quant-ph/0003079"
},
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