Symmetry Integrability and Geometry-Methods and Applications | |
Hopf Maps, Lowest Landau Level, and Fuzzy Spheres | |
article | |
Kazuki Hasebe1  | |
[1] Kagawa National College of Technology | |
关键词: division algebra; Clif ford algebra; Grassmann algebra; Hopf map; non-Abelian monopole; Landau model; fuzzy geometry; | |
DOI : 10.3842/SIGMA.2010.071 | |
来源: National Academy of Science of Ukraine | |
【 摘 要 】
This paper is a review of monopoles, lowest Landau level, fuzzy spheres, and their mutual relations. The Hopf maps of division algebras provide a prototype relation between monopoles and fuzzy spheres. Generalization of complex numbers to Clifford algebra is exactly analogous to generalization of fuzzy two-spheres to higher dimensional fuzzy spheres. Higher dimensional fuzzy spheres have an interesting hierarchical structure made of ''compounds'' of lower dimensional spheres. We give a physical interpretation for such particular structure of fuzzy spheres by utilizing Landau models in generic even dimensions. With Grassmann algebra, we also introduce a graded version of the Hopf map, and discuss its relation to fuzzy supersphere in context of supersymmetric Landau model.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
RO202106300001734ZK.pdf | 515KB | download |