Diffeomorphisms on the fuzzy sphere

• 伊敷, 吾郎

• Matsumoto, Takaki

抄録

Diffeomorphisms can be seen as automorphisms of the algebra of functions. In matrix regularization, functions on a smooth compact manifold are mapped to finite-size matrices. We consider how diffeomorphisms act on the configuration space of the matrices through matrix regularization. For the case of the fuzzy $$S^2$, we construct the matrix regularization in terms of the Berezin–Toeplitz quantization. By using this quantization map, we define diffeomorphisms on the space of matrices. We explicitly construct the matrix version of holomorphic diffeomorphisms on $$S^2$. We also propose three methods of constructing approximate invariants on the fuzzy $$S^2$. These invariants are exactly invariant under area-preserving diffeomorphisms and only approximately invariant (i.e. invariant in the large-$$N$ limit) under general diffeomorphisms.

収録刊行物

• Progress of Theoretical and Experimental Physics

  Progress of Theoretical and Experimental Physics 2020 (1), 013B04-, 2020-01

  Oxford University Press

キーワード

• General Physics and Astronomy

詳細情報

• CRID: 1050567175345753856
• NII論文ID: 120007132905
• DOI: 10.1093/ptep/ptz151
• ISSN: 20503911
• HANDLE: 2241/00161187
• Web Site: https://tsukuba.repo.nii.ac.jp/records/55783
• Web Site: http://academic.oup.com/ptep/article-pdf/2020/1/013B04/31947277/ptz151.pdf
• 本文言語コード: en
• 資料種別: journal article
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