Effective local geometric quantities in fuzzy spaces from heat kernel expansions

TL;DR

This paper extends heat kernel expansion techniques to compute local geometric quantities in fuzzy spaces, including non-associative cases, providing insights into their structure and properties.

Contribution

It introduces a generalized method for deriving local geometric quantities in fuzzy spaces, including those with non-associative algebraic structures.

Findings

Effective local geometric quantities obtained for various fuzzy spaces.

Application to fuzzy spaces with singular continuum counterparts.

Analysis of fuzzy spaces with non-associative algebraic structures.

Abstract

The heat kernel expansion can be used as a tool to obtain the effective geometric quantities in fuzzy spaces. Generalizing the efficient method presented in the previous work on the global quantities, it is applied to the effective local geometric quantities in compact fuzzy spaces. Some simple fuzzy spaces corresponding to singular spaces in continuum theory are studied as specific examples. A fuzzy space with a non-associative algebra is also studied.