Pair Correlator in the Itzykson-Zuber Integral

TL;DR

This paper derives an explicit formula for the average of pair correlators of unitary matrices under the Itzykson-Zuber measure, advancing understanding of matrix integrals in random matrix theory.

Contribution

It provides a new explicit expression for the pair correlator average over the unitary group with the Itzykson-Zuber measure.

Findings

Explicit formula for <U_{ij}U_{kl}^{}>, enhancing computational techniques.

Improved understanding of correlations in unitary matrix ensembles.

Potential applications in quantum physics and statistical mechanics.

Abstract

An explicit expression is suggested for the average $<U_{ij}U_{kl}^{\dagger}>$ over the unitary group $SU(N)$ with the Itzykson-Zuber measure $[dU] \exp {\rm tr} \Phi U\Psi U^{\dagger}$