Brian C. Hall, Jeffrey J. Mitchell
Coherent states on spheres
(104K, Latex)

ABSTRACT.  We describe a family of coherent states and an associated resolution 
of the identity for a quantum particle whose classical configuration 
space is the d-dimensional sphere S^d. The coherent states are 
labeled by points in the associated phase space T*(S^d). These 
coherent states are NOT of Perelomov type but rather are constructed 
as the eigenvectors of suitably defined annihilation operators. We 
describe as well the Segal-Bargmann representation for the system, 
the associated unitary Segal--Bargmann transform, and a natural 
inversion formula. Although many of these results are in principle 
special cases of the results of B. Hall and M. Stenzel, we give here 
a substantially different description based on ideas of T. Thiemann 
and of K. Kowalski and J. Rembielinski. All of these results can be 
generalized to a system whose configuration space is an arbitrary 
compact symmetric space. We focus on the sphere case in order 
to be able to carry out the calculations in a self-contained and 
explicit way.