Fuzzy-Space Engineering

TL;DR

This paper explores representing fuzzy surfaces using matrix models and graph techniques, demonstrating quantization of complex shapes like the Trefoil knot and enhancing visualization in fuzzy geometry.

Contribution

It introduces a method to construct and analyze fuzzy surfaces via graph-based matrices and software tools, advancing visualization and understanding of fuzzy spaces.

Findings

Quantization of a two-dimensional Trefoil knot

Development of a graph-to-matrix generation script

Insights into properties of fuzzy zero-mode surfaces

Abstract

The techniques developed for matrix models and fuzzy geometry are powerful tools for representing strings and membranes in quantum physics. We study the representation of fuzzy surfaces using these techniques. This involves constructing graphs and writing their coordinates and connectivity into matrices. To construct arbitrary graphs and quickly change them, we use 3D software. A script generates the three matrices from the graphs. These matrices are then processed in Wolfram Mathematica to calculate the zero modes of the Dirac operator. Our first result shows the quantization of a two-dimensional Trefoil knot. Additional examples illustrate various properties and behaviors of this process. This helps us to gain a deeper understanding of fuzzy spaces and zero-mode surfaces. This work contributes to advancing the understanding of visualization aspects in fuzzy geometry.