Geometrical quantities on a fuzzy sphere

TL;DR

This paper investigates geometrical properties like area and dimension on a fuzzy sphere using spectral methods, revealing their dependence on the energy scale, unlike in the classical sphere.

Contribution

It introduces a spectral approach to analyze geometrical quantities on the fuzzy sphere and uncovers their energy scale dependence, which is a novel insight.

Findings

Area and dimension depend on the energy scale.

Spectral methods effectively analyze fuzzy geometries.

Contrasts with classical sphere properties.

Abstract

In this paper, we consider the geometrical quantities on the fuzzy sphere from the spectral point of view, such as the area and the dimension. We find that, in contract to the standard sphere, the area and the dimension are the functions of the energy scale of the fuzzy sphere.