By Syed Twareque Ali,Jean-Pierre Antoine,Jean-Pierre Gazeau
This moment version is totally up-to-date, overlaying specifically new forms of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now usually in quantum optics) and diverse generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.). furthermore, it features a new bankruptcy on coherent nation quantization and the similar probabilistic elements. 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 technique permits the consumer to take a classical-like view of quantum states in physics.
Starting from the traditional conception of coherent states over Lie teams, the authors generalize the formalism by means of associating coherent states to staff representations which are sq. integrable over a homogeneous area; yet another step permits one to dispense with the crowd context altogether. during this context, wavelets may be generated from coherent states of the affine staff of the true line, and higher-dimensional wavelets come up from coherent states of different teams. The unified historical past makes obvious a whole variety of houses of wavelets and coherent states. Many concrete examples, reminiscent of 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 publication 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 concepts for use in info processing.
Intended as an advent to present learn for graduate scholars and others getting into the sector, the mathematical dialogue is self-contained. With its vast references to the study literature, the 1st version of the booklet is already a confirmed compendium for physicists and mathematicians lively within the box, and with complete insurance of the newest conception and effects the revised moment version is much more valuable.
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