Square integrability of group representations on homogeneous spaces. 2. Coherent and quasi-coherent states - The case of the Poincaré group
(1991) Institut Henri Poincare. Annales: Physique Theorique — Vol. 55, n° 4, p. 857-890 (1991)
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- Authors
Antoine, Jean-Pierre 
- Abstract
- The concept of a reproducing triple, developed in the first paper of the series (I), is utilized to give a general definition of a square integrable representation of a group. This definition is applicable to homogeneous spaces of the group, and generalizes earlier attempts at obtaining such notions. Among others, it leads naturally to a notion of equivalence among families of coherent states, and also to the concept of quasi-coherent states, or weighted coherent states. The general considerations are applied to the specific example of the Wigner representation of the Poincaré group P+up (1, 1) in one space and one time dimensions. A whole class of equivalent families of coherent states is derived, each of which corresponds to a continuous frame, in the sense of I.
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Citations
Ali, ST., Antoine, J.-P., & Gazeau, JP. (1991). Square integrability of group representations on homogeneous spaces. 2. Coherent and quasi-coherent states - The case of the Poincaré group. Institut Henri Poincare. Annales: Physique Theorique, 55(4), 857-890. https://hdl.handle.net/2078.5/26247 (Original work published 1991)