Factorizations and Physical Representations

Details Factorizations and Physical Representations Factorizations and Physical Representations

2005-08-25

arxiv.org/abs/quant-ph/0508191v1

Physics

Quantum Physics

Scientific paper

10.1088/0305-4470/39/18/027

A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (J. Zak, Phys. Today, {\bf 23} (2), 51 (1970)), and related representations termed $q_{1}q_{2}$ representations (together with their conjugates) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M.

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