K\"{a}hler structure in the commutative limit of matrix geometry

TL;DR

This paper explores how certain matrix geometries, in the limit of large matrices, naturally develop a Kähler structure, linking matrix configurations to geometric and quantization frameworks.

Contribution

It demonstrates that the commutative limit of matrix geometries inherently has a Kähler structure and establishes explicit relations between matrix configurations and geometric quantization.

Findings

The commutative limit of matrix geometry possesses a Kähler structure.

Explicit relations are derived between matrix configurations and Kähler geometry.

Connections to geometric quantization are established.

Abstract

We consider the commutative limit of matrix geometry described by a large-$N$ sequence of some Hermitian matrices. Under some assumptions, we show that the commutative geometry possesses a K\"{a}hler structure. We find an explicit relation between the K\"{a}hler structure and the matrix configurations which define the matrix geometry. We also find a relation between the matrix configurations and those obtained from the geometric quantization.