Quantum Real Lines,Infinitesimal Structure of $\R$
Abstract
We present in this paper quantum real lines as quantum defomations of the real numbers $\R$.Upon deforming the Heisenberg algebra $\cL$ generated by $(a, a^\dagger)$ in terms of the Moyal $\ast$product,we first construct qdeformed algebras of qdifferentiable functions in two cases where q is generic (not a root of unity) and q is the Nth 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2002
 DOI:
 10.48550/arXiv.hepth/0205226
 arXiv:
 arXiv:hepth/0205226
 Bibcode:
 2002hep.th....5226S
 Keywords:

 High Energy Physics  Theory
 EPrint:
 21 pages, Latex2e