• Corpus ID: 118982146

Quantum Real Lines,Infinitesimal Structure of $\R$

  title={Quantum Real Lines,Infinitesimal Structure of \$\R\$},
  author={Takashi Suzuki},
  journal={arXiv: High Energy Physics - Theory},
  • Takashi Suzuki
  • Published 22 May 2002
  • Mathematics
  • arXiv: High Energy Physics - Theory
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… 

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