The matrix regularization for Riemann surfaces with magnetic fluxes

Abstract

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.

arXiv comment42 pages, 1 figure; v3: some references and 1 figure with some comments added, minor modifications

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Cited by in corpus (2)

• Laplacians on Fuzzy Riemann Surfaces
• Deformation of Matrix Geometry via Landau Level Evolution