Laplacians on Fuzzy Riemann Surfaces
Hiroyuki Adachi, Goro Ishiki, Satoshi Kanno, Takaki Matsumoto
TL;DR
This paper develops a fuzzy version of the Laplacian operator on Riemann surfaces with gauge fields, using matrix regularization of scalar fields, advancing the mathematical tools for noncommutative geometry.
Contribution
It introduces a novel construction of the fuzzy Laplacian on Riemann surfaces with gauge backgrounds, extending noncommutative geometric methods.
Findings
Constructed a fuzzy Laplacian compatible with gauge fields.
Provided a matrix regularization framework for scalar fields.
Enhanced the mathematical understanding of fuzzy Riemann surfaces.
Abstract
We consider the matrix regularization of scalar fields on a Riemann surface with a general gauge-field background. We propose a construction of the fuzzy version of the Laplacian.
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