2021-09-29T03:23:10Zhttps://tsukuba.repo.nii.ac.jp/oaioai:tsukuba.repo.nii.ac.jp:000557832021-03-01T12:25:47ZDiffeomorphisms on the fuzzy sphere伊敷, 吾郎イシキ, ゴロウISHIKI, GoroMatsumoto, TakakiDiffeomorphisms 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\n$$S^2$, we construct the matrix regularization in terms of the Berezin–Toeplitz quantization. By using this quantization map, we define diffeomorphisms on the space of matrices. We explicitly construct the matrix version of holomorphic diffeomorphisms on $$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.journal articleOxford University Press2020-01application/pdfProgress of Theoretical and Experimental Physics12020013B042050-3911https://tsukuba.repo.nii.ac.jp/record/55783/files/PTEP_2020-1.pdfeng10.1093/ptep/ptz151Originally published in Progress of Theoretical and Experimental Physics, 2020, 013B04 © The Author(s) 2020. Published by Oxford University Press on behalf of the Physical Society of Japan. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. Funded by SCOAP3