Nevertheless, separated from their respective applications, coherent states and continuous wavelets have a great deal in common. However, they have generated a huge variety of generalizations, which have led to a tremendous literature in mathematical physics. Coherent states in a magnetic field and their generalizations. We provide copy of coherent states wavelets and their. Although this talk is meant to illustrate the theory of coherent states and wavelets by. In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects.
Joint ictptwas school on coherent state transforms, timefrequency and timescale analysis, applications jp. In addition, it contains a new chapter on coherent state. Contents 1 preliminaries contents references 2 canonical coherent states 3 some interesting properties of the canonical cs 4 an application and outlook s. The construction follows a general method based on square integrable group representations, possibly modulo a subgroup, i.
References syed twareque ali, jeanpierre antoine, and jeanpierre gazeau. Request pdf coherent stateswavelets and their generalizations this second edition is fully updated, covering in particular new types of coherent states. Coherent states, wavelets, and their generalizations this second edition is fully updated, covering in particular new types of coherent states the socalled gazeauklauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics and various generalizations of wavelets wavelets on manifolds. We address our presentation to interested wavelet practitioners. The inverse source problem for wavelet fields with a j devaney, a marengo, r albanese, and g erdmann. Let us note that in the signal analysis literature, the canonical coherent states are known as gaborettes or gabor wavelets. Coherent states and their generalizations a mathematical. Pdf coherent states and their generalizations a mathematical. Starting from the standard theory of coherent states over lie groups, the. Although the main attention is paid to the gaussian states, various families of nongaussian states are also discussed, and the list of relevant references is provided.
Generalized huygens principle with pulsedbeam wavelets with thorkild hansen, j. Centre ville montrdal qudbec, h3c 3j7 canada abstract. This book presents a survey of the theory of coherent states, wavelets, and some of their generalizations, emphasizing mathematical structures. Coherent states, povm, quantization and measurement. Mueller 4 1 department of mathematics and statistics, concordia. If you are looking for coherent states wavelets and their generalizations 1st edition, our library is free for you. Coherent states for a gener alization of the harmonic oscillator david j.
The point of view is that the theories of wavelets and coherent states can both be subsumed into a single mathematical structure. Coherent states, wavelets and their generalizations by syed twareque ali, jeanpierre antoine and jeanpierre gazeau no static citation data no static citation data cite. Coherent states have been introduced in a physical context, first as quasiclassical states in quantum mechanics, then as the backbone of quantum optics and they are described in that spirit in the article coherent states see also. Coherent states, wavelets, and their generalizations syed. Under gazeaus initiative, supported by several colleagues, the university in. Syed twareque ali, jeanpierre antoine, jeanpierre gazeau auth. Gazeau is the author coherent states in quantum physics 2009. This lecture will recount some of the salient episodes belonging in the earlier part of this sagaand bow out at the threshold of the history of wavelets proper, thus focusing on the hatching grounds provided by coherent states. Coherent stateswavelets and their generalizations request pdf. He is the coauthor of coherent states, wavelets and their generalizations, initially published in 2000 with a revised edition in 2014. Quantum measurement theoretical and mathematical physics. Starting from the standard theory of cs over lie groups, we develop a general formalism, in which cs are associated to group representations which are square integrable over a homogeneous space. Twareque ali department of mathematics and statistics concordia university montr eal, qu ebec, canada h3g 1m85pt coherent states and wavelets.
Coherent states, wavelets, and their generalizations ebook. Second edition just appeared, november 20 first prev next last go back full screen. Coherent states and wavelets, a contemporary panorama. We present a survey of the theory of coherent states cs. Wavelets in applied and pure mathematics\ postgraduate. Coherent states, wavelets, and their generalizations theoretical and mathematical physics categories. To illustrate this connection we shall outline three general types of coherent states and a few of their applications. At paris diderot university, gazeau served as vice president for communication from 19921997. As a survey of the theory of coherent states, wavelets, and some of their generalizations, it emphasizes mathematical principles, subsuming the theories of both wavelets and coherent states into a single analytic structure. Coherent states, wavelets and their generalizations graduate texts in mathematics, springer, new york, 2000. Coherent states, wavelets, and their generalizations graduate texts in contemporary physics author. Coherent states, wavelets and their generalizations core. A survey of the theory of coherent states, wavelets, and some of their generalizations, emphasizing mathematical structures.
It was the first example of quantum dynamics when erwin schrodinger derived it in 1926, while searching for solutions of the. Generalizations, second edition, springerverlag, new york. Coherent states, wavelets and their generalizations syed. The approach allows the user to take a classicallike view of quantum states in physics. In physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a state which has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator. Coherent states, wavelets and their generalizations. Pdf we present a survey of the theory of coherent states cs and some of their. Basic real and complex analysis, rudimentary algebra. Coherent electromagnetic wavelets and their twisting null congruences. Coherent states, wavelets and their generalizations guide books.
Syed twareque ali, jeanpierre antoine, jeanpierre gazeau. Coherent states, wavelets, and their generalizations. Abstract we present a survey of the theory of coherent states cs and some of their gen eralizations, with emphasis on the mathematical structure, rather than on physical applications. International journal of wavelets, multiresolution and information processing vol. Next, we describe the construction of a cwt on the upper sheet of a twosheeted hyperboloid, emphasizing the similarities between the two cases. The point of view is that both the theories of both wavelets and coherent states can be subsumed into a single analytic structure. We derive galilean wavelets, by which we mean coherent states of the affine galilei group, that is, the galilei group extended by independent space and time dilations. Coherent states, wavelets, and their generalizations springerlink. Starting from the standard theory of coherent states over lie groups, the authors generalize the formalism by associating coherent states to group representations that are square integrable over a homogeneous space.
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