2003/11/17 by Takashi Suzuki, Suzuki, Takashi
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0311140
23 pages, no figures
arxiv created 2003/11/17 · arxiv updated 2009/12/01
Quantum real numbers are proposed by performing a quantum deformation of the standard real numbers \R. We start with the q-deformed Heisenberg algebra \cLLq which is obtained by the Moyal ∗-deformation of the Heisenberg algebra generated by a and \ad. By representing \cLLq as the algebras of q-differentiable functions, we derive quantum real lines from the base spaces of these functional algebras. We find that these quantum lines are discrete spaces. In particular, for the case with q = e2πi (1)/(N) , the quantum real line is composed of fuzzy, i.e., fluctuating points and nontrivial infinitesimal structure appears around every standard real number.