2020/02/29 by Hiroyuki Adachi, Goro Ishiki, Takaki Matsumoto +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Computer science #Diagonalizable matrix #Eigenvalues and eigenvectors #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Laplace operator #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Matrix function #Physics #Pure mathematics #Quantum mechanics #Regularization (linguistics) #Riemann hypothesis #Riemann surface #Symmetric matrix #Zeta function regularization #hep-th
paper · pdf · doi:10.1103/physrevd.101.106009
published as Phys. Rev. D 101, 106009 (2020) · 42 pages, 1 figure; v3: some references and 1 figure with some comments added, minor modifications
arxiv created 2020/05/06 · openalex publication_date 2020/05/08 · arxiv updated 2020/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the matrix regularization of fields on a Riemann surface which couple to gauge fields with a nonvanishing magnetic flux. We show that such fields are described as rectangular matrices in the matrix regularization. We construct the matrix regularization explicitly for the case of the sphere and torus based on the Berezin-Toeplitz quantization, and also discuss a possible generalization to cases with higher genera. We also discuss the matrix version of the Laplacian acting on the rectangular matrices.