dorsal/arxiv
View SchemaHyperfinite-Dimensional Representations of Canonical Commutation Relation
| Authors | Hideyasu Yamashita |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9706008 |
| URL | https://arxiv.org/abs/quant-ph/9706008 |
| DOI | 10.1063/1.532413 |
| Journal | J.Math.Phys. 39 (1998) 2682-2692 |
Abstract
This paper presents some methods of representing canonical commutation relations in terms of hyperfinite-dimensional matrices, which are constructed by nonstandard analysis. The first method uses representations of a nonstandard extension of finite Heisenberg group, called hyperfinite Heisenberg group. The second is based on hyperfinite-dimensional representations of so(3). Then, the cases of infinite degree of freedom are argued in terms of the algebra of hyperfinite parafermi oscillators, which is mathematically equivalent to a hyperfinite-dimensional representation of so(n).
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"abstract": "This paper presents some methods of representing canonical commutation\nrelations in terms of hyperfinite-dimensional matrices, which are constructed\nby nonstandard analysis. The first method uses representations of a nonstandard\nextension of finite Heisenberg group, called hyperfinite Heisenberg group. The\nsecond is based on hyperfinite-dimensional representations of so(3). Then, the\ncases of infinite degree of freedom are argued in terms of the algebra of\nhyperfinite parafermi oscillators, which is mathematically equivalent to a\nhyperfinite-dimensional representation of so(n).",
"arxiv_id": "quant-ph/9706008",
"authors": [
"Hideyasu Yamashita"
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"doi": "10.1063/1.532413",
"journal_ref": "J.Math.Phys. 39 (1998) 2682-2692",
"title": "Hyperfinite-Dimensional Representations of Canonical Commutation Relation",
"url": "https://arxiv.org/abs/quant-ph/9706008"
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