On a Bargmann transform and coherent states for the n-sphere

Analysis Seminar
Wednesday, November 4, 2009 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 269
Dr Carlos Villegas Blas – Instituto de Matematicas UNAM, Unidad. Cuernavaca – villegas@matcuer.unam.mxhttp://www.matcuer.unam.mx/personal.php?id=32
Jean Bellissard
We will introduce a Bargmann transform from the space of square integrable functions on the n-sphere onto a suitable Hilbert space of holomorphic functions on a null quadric. On base of our Bargmann transform, we will introduce a set of coherent states and study their semiclassical properties. For the particular cases n=2,3,5, we will show the relation with two known regularizations of the Kepler problem: the Kustaanheimo-Stiefel and Moser regularizations.