Matrix regularization for tensor fields

We propose a novel matrix regularization for tensor fields. In this regularization, tensor fields are described as rectangular matrices, and area-preserving diffeomorphisms and local rotations of the orthonormal frame are both realized as unitary similarity transformations of matrices in a unified w...

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Published inProgress of theoretical and experimental physics Vol. 2023; no. 1
Main Authors Adachi, Hiroyuki, Ishiki, Goro, Kanno, Satoshi, Matsumoto, Takaki
Format Journal Article
LanguageEnglish
Published Oxford Oxford University Press 01.01.2023
Subjects
Vector space
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Summary:We propose a novel matrix regularization for tensor fields. In this regularization, tensor fields are described as rectangular matrices, and area-preserving diffeomorphisms and local rotations of the orthonormal frame are both realized as unitary similarity transformations of matrices in a unified way. We also show that the matrix commutator corresponds to the covariantized Poisson bracket for tensor fields in the large-N limit.
Bibliography:ObjectType-Article-1
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ISSN:2050-3911
2050-3911
DOI:10.1093/ptep/ptac171