Some Complex Quantum Manifolds and their Geometry

Chong-Sun Chu; Pei-Ming Ho; Bruno Zumino

Some Complex Quantum Manifolds and their Geometry

高能物理 - 理论 2007-05-23 v1

作者: Chong-Sun Chu , Pei-Ming Ho , Bruno Zumino

摘要

After recalling briefly some basic properties of the quantum group $GL_q(2)$ , we study the quantum sphere $S_q^2$ , quantum projective space $CP_q(N)$ and quantum Grassmannians as examples of complex (K\"{a}hler) quantum manifolds. The differential and integral calculus on these manifolds are discussed. It is shown that many relations of classical projective geometry generalize to the quantum case. For the case of the quantum sphere a comparison is made with A. Connes' method.

关键词

quantum algebra differential geometry in physics quantum gravity

引用

@article{arxiv.hep-th/9608188,
  title  = {Some Complex Quantum Manifolds and their Geometry},
  author = {Chong-Sun Chu and Pei-Ming Ho and Bruno Zumino},
  journal= {arXiv preprint arXiv:hep-th/9608188},
  year   = {2007}
}

备注

Cargese lectures, July 1996, one figure, Full postscript available from http://theor1.lbl.gov/www/theorgroup/papers/39275.ps

Some Complex Quantum Manifolds and their Geometry

摘要

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