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Coherent states of the Poincaré group, related frames and transforms

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Coherent states of the Poincaré group, related frames and transforms

Karim, Mohammed Rezaul (1996) Coherent states of the Poincaré group, related frames and transforms. PhD thesis, Concordia University.

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Abstract

We construct here families of coherent states for the full Poincare group, for representations corresponding to mass $m>0$ and arbitrary integral or half-integral spin. Each family of coherent states is defined by an affine section in the group and constitutes a frame. The sections, in their turn, are determined by particular velocity vector fields, the latter always appearing in dual pairs. We discretize the coherent states of Poincare group in 1-space and 1-time dimensions and show that they form a discrete frame, develop a transform, similar to a windowed Fourier transform, which we call the relativistic windowed Fourier transform. We also obtain a reconstruction formula. Finally, we perform numerical computations. We evaluate the discrete frame operator numerically and present it graphically for different sections and windows. We also reconstruct some functions, compare reconstructed functions with the original ones graphically. We compare the reconstruction scheme of the relativistic windowed Fourier transform with that of the standard windowed Fourier transform.

Divisions:Concordia University > School of Graduate Studies
Item Type:Thesis (PhD)
Authors:Karim, Mohammed Rezaul
Pagination:viii, 115 leaves : ill. ; 29 cm.
Institution:Concordia University
Degree Name:Theses (Ph.D.)
Program:Special Individualized Programme
Date:1996
Thesis Supervisor(s):Ali, S. Twareque
ID Code:241
Deposited By:Concordia University Libraries
Deposited On:27 Aug 2009 13:10
Last Modified:08 Dec 2010 10:13
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