By Syed Twareque Ali,Jean-Pierre Antoine,Jean-Pierre Gazeau
This moment version is totally up to date, overlaying particularly new kinds of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now often in quantum optics) and numerous generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.). additionally, it includes a new bankruptcy on coherent kingdom quantization and the similar probabilistic facets. As a survey of the idea of coherent states, wavelets, and a few in their generalizations, it emphasizes mathematical ideas, subsuming the theories of either wavelets and coherent states right into a unmarried analytic constitution. The process permits the person to take a classical-like view of quantum states in physics.
Starting from the traditional idea of coherent states over Lie teams, the authors generalize the formalism via associating coherent states to staff representations which are sq. integrable over a homogeneous house; yet another step permits one to dispense with the gang context altogether. during this context, wavelets will be generated from coherent states of the affine team of the genuine line, and higher-dimensional wavelets come up from coherent states of alternative teams. The unified history makes obvious a complete diversity of houses of wavelets and coherent states. Many concrete examples, similar to coherent states from semisimple Lie teams, Gazeau-Klauder coherent states, coherent states for the relativity teams, and several other varieties of wavelets, are mentioned intimately. The ebook concludes with a palette of potential applications, from the quantum bodily oriented, like the quantum-classical transition or the development of enough states in quantum info, to the main cutting edge strategies for use in info processing.
Intended as an advent to present learn for graduate scholars and others coming into the sector, the mathematical dialogue is self-contained. With its huge references to the learn literature, the 1st variation of the ebook is already a confirmed compendium for physicists and mathematicians energetic within the box, and with complete assurance of the newest concept and effects the revised moment version is much more valuable.
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Coherent States, Wavelets, and Their Generalizations (Theoretical and Mathematical Physics) by Syed Twareque Ali,Jean-Pierre Antoine,Jean-Pierre Gazeau
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