Factorizations and Physical Representations
Quantum Physics
2009-11-11 v1
Abstract
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 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.
Cite
@article{arxiv.quant-ph/0508191,
title = {Factorizations and Physical Representations},
author = {M. Revzen and F. C. Khanna and A. Mann and J. Zak},
journal= {arXiv preprint arXiv:quant-ph/0508191},
year = {2009}
}