Quantum Real Lines,Infinitesimal Structure of $\R$

Details Quantum Real Lines,Infinitesimal Structure of $\R$ Quantum Real Lines,Infinitesimal Structure of $\R$

2002-05-22

arxiv.org/abs/hep-th/0205226v1

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, Latex2e

Scientific paper

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 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.

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