Matrix regularization for tensor fields. (13th December 2022)

• Record Type: Journal Article
• Authors: Adachi, Hiroyuki; Ishiki, Goro; Kanno, Satoshi; Matsumoto, Takaki
• Is Part Of: Progress of theoretical and experimental physics. Volume 2023:Number 1(2023)
• Publication Date: 2022-12-13
• Subjects: Physics -- Periodicals; Mathematical physics -- Periodicals; 530.05
• DOI: 10.1093/ptep/ptac171
• Languages: English
• ISSNs: 2050-3911

Abstract

Abstract: 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.