 01330 Brian C. Hall, Jeffrey J. Mitchell
 Coherent states on spheres
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Sep 18, 01

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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 ddimensional 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 SegalBargmann representation for the system,
the associated unitary SegalBargmann 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 selfcontained and
explicit way.
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