Characterization of SU(1,1) coherent states in terms of affine group wavelets
Jacqueline Bertrand, Michele Irac-Astaud (Universite Paris VII)
TL;DR
This paper links SU(1,1) coherent states to affine group wavelets by exploiting the isomorphism between the quotient space and the affine group, revealing new properties and parametrizations.
Contribution
It introduces a novel parameterization of SU(1,1) coherent states using affine group elements, connecting quantum states with wavelet theory.
Findings
New properties of SU(1,1) coherent states identified
Parameterization of states via affine group points
Relation established between coherent states and affine wavelets
Abstract
The Perelomov coherent states of SU(1,1) are labeled by elements of the quotient of SU(1,1) by the compact subgroup. Taking advantage of the fact that this quotient is isomorphic to the affine group of the real line, we are able to parameterize the coherent states by elements of that group or equivalently by points in the half-plane. Such a formulation permits to find new properties of the SU(1,1) coherent states and to relate them to affine wavelets.
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