General approach to SU(n) quasi-distribution functions

TL;DR

This paper introduces a new method for mapping quantum operators with SU(n) symmetry to classical phase space symbols, providing a bijective correspondence for symmetric irreducible representations, and discusses potential complications in the general case.

Contribution

It presents an operational kernel form for the SU(n) operator-to-symbol mapping, enhancing the understanding of phase space representations in quantum systems with SU(n) symmetry.

Findings

Bijective mapping for symmetric irreps of SU(n)

Operational kernel form for the operator-symbol mapping

Discussion of complications in the general case

Abstract

We propose an operational form for the kernel of a mapping between an operator acting in a Hilbert space of a quantum system with SU(n) symmetry group and its symbol in the corresponding classical phase space. For symmetric irreps of SU(n), this mapping is bijective. We briefly discuss complications that will occur in the general case.