Proof of the Wehrl-type Entropy Conjecture for Symmmetric SU(N) Coherent States

TL;DR

This paper proves a conjecture that highest weight states minimize certain entropy-related integrals in symmetric representations of SU(N), extending previous results from Heisenberg and SU(2) groups.

Contribution

It extends the Wehrl entropy conjecture proof to symmetric SU(N) representations for all N, broadening the understanding of entropy minimization in Lie group representations.

Findings

Proves Wehrl entropy conjecture for symmetric SU(N) states

Shows highest weight states minimize group integrals of concave functions

Extends previous results from Heisenberg and SU(2) groups

Abstract

The Wehrl entropy conjecture for coherent (highest weight) states in representations of the Heisenberg group, which was proved in 1978 and recently extended by us to the group $SU(2)$, is further extended here to symmetric representations of the groups $SU(N)$ for all $N$. This result gives further evidence for our conjecture that highest weight states minimize group integrals of certain concave functions for a large class of Lie groups and their representations.