New Methods of Integration in Matrix Models

TL;DR

The paper introduces a novel integration method for matrix models that simplifies calculations by decoupling angular variables, facilitating easier computation of correlation functions and eigenvalue reductions.

Contribution

It presents a new gauge-based integration technique that simplifies multi-matrix model analysis and provides a straightforward proof of classical eigenvalue reduction formulas.

Findings

Decouples angular variables in certain two-matrix models

Simplifies correlation function calculations

Provides a simple proof of eigenvalue reduction formula

Abstract

We discuss a new method of integration over matrix variables based on a suitable gauge choice in which the angular variables decouple from the eigenvalues at least for a class of two-matrix models. The calculation of correlation functions involving angular variables is simple in this gauge. Where the method is applicable it also gives an extremely simple proof of the classical integration formula used to reduce multi-matrix models to an integral over the eigenvalues.