Matrix Geometry and Coherent States

TL;DR

This paper introduces a method to derive classical geometric spaces from matrix models by constructing coherent states, enabling the analysis of geometric properties directly from matrix configurations.

Contribution

It presents a novel approach to extract classical geometry from matrix models using coherent states, linking matrix elements to geometric objects.

Findings

Defines coherent states for matrix geometries.

Expresses geometric objects like metric and curvature in matrix terms.

Provides a new class of observables for matrix models.

Abstract

We propose a novel method of finding the classical limit of the matrix geometry. We define coherent states for a general matrix geometry described by a large-N sequence of D Hermitian matrices X_\mu (\mu =1,2, ..., D) and construct a corresponding classical space as a set of all coherent states. We also express various geometric objects on the classical space such as the metric, Levi-Civita connection, curvature and Poisson tensor, in terms of the matrix elements. This method provides a new class of observables in matrix models, which characterize geometric properties of matrix configurations.