Information metric, Berry connection, and Berezin-Toeplitz quantization for matrix geometry
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We consider the information metric and Berry connection in the context of noncommutative matrix geometry. We propose that these objects give a new method of characterizing the fuzzy geometry of matrices. We first give formal definitions of these geometric objects and then explicitly calculate them for the well-known matrix configurations of fuzzy S2 and fuzzy S4. We find that the information metrics are given by the usual round metrics for both examples, while the Berry connections coincide with the configurations of the Wu-Yang monopole and the Yang monopole for fuzzy S2 and fuzzy S4, respectively. Then, we demonstrate that the matrix configurations of fuzzy Sn (n=2, 4) can be understood as images of the embedding functions Sn→Rn+1 under the Berezin-Toeplitz quantization map. Based on this result, we also obtain a mapping rule for the Laplacian on fuzzy S4.
収録刊行物
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- Physical review D
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Physical review D 98 (2), 026002-, 2018-07
American Physical Society
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詳細情報 詳細情報について
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- CRID
- 1050282814175609344
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- NII論文ID
- 120007133536
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- NII書誌ID
- AA00773624
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- HANDLE
- 2241/00157351
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- ISSN
- 24700010
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- 本文言語コード
- en
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- 資料種別
- journal article
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- データソース種別
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- IRDB
- CiNii Articles