Wehrl-type coherent state entropy inequalities for SU(1,1) and its AX+B subgroup

2019/06/01 by Élliott H. Lieb, Lieb, Elliott H., Jan Philip Solovej +1
Mathematics · Neuroscience · Physics and Astronomy · #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Neuroscience and Neuropharmacology Research #Quantum Mechanics and Non-Hermitian Physics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1906.00223

openalex publication_date 2019/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the Wehrl-type entropy inequality conjecture for the group SU(1,1) and for its subgroup AX+B (or affine group), their representations on L²(\mathbb R₊), and their coherent states. For AX+B the Wehrl-type conjecture for L^p-norms of these coherent states (also known as the Rényi entropies) is proved in the case that p is an even integer. We also show how the general AX+B case reduces to an unsolved problem about analytic functions on the upper half plane and the unit disc.

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