Hyperfinite-Dimensional Representations of Canonical Commutation Relation

Details Hyperfinite-Dimensional Representations of Canonical Commutation Relation Hyperfinite-Dimensional Representations of Canonical Commutation Relation

1997-06-04

arxiv.org/abs/quant-ph/9706008v3

J.Math.Phys. 39 (1998) 2682-2692

Physics

Quantum Physics

18 pages, LaTeX

Scientific paper

10.1063/1.532413

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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