The Canonical Coherent States Associated With Quotients of the Affine Weyl-Heisenberg Group∗

DFG–Schwerpunktprogramm 1114 Mathematical methods for time series analysis and digital image processing The Canonical Coherent States Associated With Quotients of the Affine Weyl-Heisenberg Group

This paper is concerned with the uncertainty principle in the context of the affine-Weyl-Heisenberg group in one and two dimensions. As the representation of this group fails to be square integrable, we explore various admissible sections of this group, and calculate the resulting uncertainty principles as well as its minimizers with respect to these sections. Previous studies have shown that t...

A Necessary Condition for Weyl-Heisenberg Frames

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

ar X iv : q ua nt - p h / 03 10 14 7 v 1 2 3 O ct 2 00 3 REPRESENTATIONS OF COHERENT STATES IN NON - ORTHOGONAL BASES

Starting with the canonical coherent states, we demonstrate that all the so-called nonlinear coherent states, used in the physical literature, as well as large classes of other generalized coherent states, can be obtained by changes of bases in the underlying Hilbert space. This observation leads to an interesting duality between pairs of generalized coherent states, bringing into play a Gelfan...

Extended Voros product in the coherent states framework

Using coherent states of the Weyl-Heisenberg algebra hN , extended Voros products and Moyal brakets are derived. The covariance of Voros product under canonical transformations is discussed. Star product related to BarutGirardello coherent states of the Lie algebra su(1, 1) is also considered. The star eigenvalue problem of singular harmonic osillator is investigated.