Syed twareque ali, jeanpierre antoine, jeanpierre gazeau. The approach allows the user to take a classicallike view of quantum states in physics. In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. We provide copy of coherent states wavelets and their. Coherent states for a gener alization of the harmonic oscillator david j. Pdf we present a survey of the theory of coherent states cs and some of their.
Twareque ali department of mathematics and statistics concordia university montr eal, qu ebec, canada h3g 1m85pt coherent states and wavelets. We present a survey of the theory of coherent states cs. References syed twareque ali, jeanpierre antoine, and jeanpierre gazeau. We address our presentation to interested wavelet practitioners. Gazeau is the author coherent states in quantum physics 2009.
The point of view is that the theories of wavelets and coherent states can both be subsumed into a single mathematical structure. Coherent states, povm, quantization and measurement. Let us note that in the signal analysis literature, the canonical coherent states are known as gaborettes or gabor wavelets. Coherent states, wavelets, and their generalizations graduate texts in contemporary physics author. Although this talk is meant to illustrate the theory of coherent states and wavelets by. Wavelets in applied and pure mathematics\ postgraduate.
The point of view is that both the theories of both wavelets and coherent states can be subsumed into a single analytic structure. The construction follows a general method based on square integrable group representations, possibly modulo a subgroup, i. Syed twareque ali, jeanpierre antoine, jeanpierre gazeau auth. The use of wavelets in research and technology has witnessed explosive growth in recent years, while the use of coherent states in numerous areas of theoretical and experimental physics has been an established trend for decades.
Joint ictptwas school on coherent state transforms, timefrequency and timescale analysis, applications jp. International journal of wavelets, multiresolution and information processing vol. However, they have generated a huge variety of generalizations, which have led to a tremendous literature in mathematical physics. We present a survey of the theory of coherent states cs and some of their generalizations, with emphasis on the mathematical structure, rather than on physical applications. To illustrate this connection we shall outline three general types of coherent states and a few of their applications. 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. 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.
Nevertheless, separated from their respective applications, coherent states and continuous wavelets have a great deal in common. Coherent states, wavelets, and their generalizations syed. In addition, it contains a new chapter on coherent state. 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. The inverse source problem for wavelet fields with a j devaney, a marengo, r albanese, and g erdmann. Basic real and complex analysis, rudimentary algebra. Coherent stateswavelets and their generalizations request pdf. 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. A survey of the theory of coherent states, wavelets, and some of their generalizations, emphasizing mathematical structures. 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. Request pdf coherent stateswavelets and their generalizations this second edition is fully updated, covering in particular new types of coherent states.
Second edition just appeared, november 20 first prev next last go back full screen. Coherent states, wavelets and their generalizations ebook. Coherent states, wavelets and their generalizations guide books. Coherent states in a magnetic field and their generalizations. He is the coauthor of coherent states, wavelets and their generalizations, initially published in 2000 with a revised edition in 2014. Coherent states, wavelets, and their generalizations springerlink. Quantum measurement theoretical and mathematical physics. Pdf coherent states and their generalizations a mathematical. Coherent states, wavelets and their generalizations by syed twareque ali, jeanpierre antoine and jeanpierre gazeau no static citation data no static citation data cite. This book presents a survey of the theory of coherent states, wavelets, and some of their generalizations, emphasizing mathematical structures. Coherent states, wavelets, and their generalizations ebook. This book presents 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. Next, we describe the construction of a cwt on the upper sheet of a twosheeted hyperboloid, emphasizing the similarities between the two cases. 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. 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 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. In addition, it contains a new chapter on coherent state quantization. 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. Generalizations, second edition, springerverlag, new york. Coherent states, wavelets, and their generalizations theoretical and mathematical physics categories.
Centre ville montrdal qudbec, h3c 3j7 canada abstract. At paris diderot university, gazeau served as vice president for communication from 19921997. Coherent states, wavelets and their generalizations graduate texts in mathematics, springer, new york, 2000. Coherent electromagnetic wavelets and their twisting null congruences. Under gazeaus initiative, supported by several colleagues, the university in. Coherent states, wavelets and their generalizations. Coherent states and wavelets, a contemporary panorama. Coherent states, wavelets, and their generalizations. Coherent states, wavelets and their generalizations core. Contents 1 preliminaries contents references 2 canonical coherent states 3 some interesting properties of the canonical cs 4 an application and outlook s.
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