2004/07/31 by N. Mukunda, G. Marmo, A. Zampini +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Spectral Theory in Mathematical Physics #quant-ph
paper · pdf · doi:10.1063/1.1825078
published as J.Math.Phys. 46 (2005) 012106 · 32 pages, Latex2e
arxiv created 2004/08/02 · openalex publication_date 2005/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The Wigner–Weyl isomorphism for quantum mechanics on a compact simple Lie group G is developed in detail. Several features are shown to arise which have no counterparts in the familiar Cartesian case. Notable among these is the notion of a semiquantized phase space, a structure on which the Weyl symbols of operators turn out to be naturally defined and, figuratively speaking, located midway between the classical phase space T*G and the Hilbert space of square integrable functions on G. General expressions for the star product for Weyl symbols are presented and explicitly worked out for the angle-angular momentum case.