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

  • Elliott H. Lieb

    Princeton University, USA
  • Jan Philip Solovej

    University of Copenhagen, Denmark
Wehrl-type coherent state entropy inequalities for SU(1,1) and its $AX+B$ subgroup cover
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Abstract

We discuss the Wehrl-type entropy inequality conjecture for the group SU(1,1)\mathrm{SU}(1,1) and for its subgroup AX+BAX+B (or affine group), their representations on L2(R+)L^2(\mathbb{R}_+), and their coherent states. For AX+BAX+B the Wehrl-type conjecture for LpL^p-norms of these coherent states (also known as the Renyi entropies) is proved in the case that pp is an even integer. We also show how the general AX+BAX+B case reduces to an unsolved problem about analytic functions on the upper half-plane and the unit disk.