Hyperfinite-dimensional representations of canonical commutation relation | Zendy

Hideyasu Yamashita | Zendy

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Hyperfinite-dimensional representations of canonical commutation relation

Author(s) -

Hideyasu Yamashita

Publication year - 1998

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.532413

Subject(s) - mathematics , pure mathematics , extension (predicate logic) , representation (politics) , algebra over a field , commutation , quantum mechanics , physics , voltage , politics , computer science , political science , law , programming language

This paper presents some methods of representing canonical commutationrelations in terms of hyperfinite-dimensional matrices, which are constructedby nonstandard analysis. The first method uses representations of a nonstandardextension of finite Heisenberg group, called hyperfinite Heisenberg group. Thesecond is based on hyperfinite-dimensional representations of so(3). Then, thecases of infinite degree of freedom are argued in terms of the algebra ofhyperfinite parafermi oscillators, which is mathematically equivalent to ahyperfinite-dimensional representation of so(n).Comment: 18 pages, LaTe

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