2002/05/22 by Takashi Suzuki, Suzuki, Takashi
Computer Science · Mathematics · Physics and Astronomy · #Advanced Algebra and Logic #Mathematical and Theoretical Analysis #advanced mathematical theories #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0205226
21 pages, Latex2e
arxiv created 2002/05/22 · arxiv updated 2009/11/30
We present in this paper quantum real lines as quantum defomations of the real numbers \R.Upon deforming the Heisenberg algebra \cL generated by (a, a^†) in terms of the Moyal ∗-product,we first construct q-deformed algebras of q-differentiable functions in two cases where q is generic (not a root of unity) and q is the N-th root of unity. We then investigate these algebras and finally propose two quantum real lines as the base spaces of these algebras. It is turned out that both quantum lines are discrete spaces and have noncommutative structures.We further find, minimal length, fuzzy structure and infinitesimal structure.