# Correspondence rules for Wigner functions over SU(3)/U(2)

## TL;DR

This paper derives differential correspondence rules for the * product of Wigner functions over the SU(3)/U(2) space, highlighting their unique second-order derivative structure compared to other cases.

## Contribution

It provides the first explicit form of the * product correspondence rules for SU(3) Wigner functions, especially when involving su(3) generators.

## Key findings

- Derived differential form of the * product for SU(3) Wigner functions.
- Showed that the rules involve second order derivatives.
- Highlighted differences from known cases in quantum phase space.

## Abstract

We present results on the * product for SU(3) Wigner functions over SU(3)/U(2). In particular, we present a form of the so-called correspondence rules, which provide a differential form of the * product A*B and A*B when A is an su(3) generator. For the su(3) Wigner map, these rules must contain second order derivatives and thus substantially differ from the rules of other known cases.