Coherent states on spheres

Details Coherent states on spheres Coherent states on spheres

2001-09-18

arxiv.org/abs/quant-ph/0109086v2

J.Math.Phys. 43 (2002) 1211-1236; Erratum-ibid. 46 (2005) 059901

Physics

Quantum Physics

Revised version. Submitted to J. Mathematical Physics

Scientific paper

10.1063/1.1446664

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.

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