Square integrability of group representations on homogeneous spaces and generalized coherent states. (English) Zbl 0761.22022

Ali, S. Twareque; Antoine, J.-P.; Gazeau, J.-P.

Geometry and physics, Proc. Winter Sch., Srni/Czech. 1990, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 26, 47-56 (1991).

[For the entire collection see Zbl 0742.00067.]
The authors develop a much more general formalism of constructing coherent states compared with the standard one where the so called admissibility condition is required, and its generalization given by Perelomov. The latter becomes inapplicable to the Galilei group or Poincaré groups. The formalism is illustrated by the direct derivation of constructing systems of coherent states for the 1+1 dimensional Poincaré group.

Reviewer: E.Kryachko (München)

MSC:

22E70	Applications of Lie groups to the sciences; explicit representations
22D10	Unitary representations of locally compact groups
81R30	Coherent states

Keywords:

locally compact; group representation; coherent states; Poincaré group

Citations:

Zbl 0742.00067