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Author: S Twareque Ali
Publisher: World Scientific
Published: 1993-10-29
Total Pages: 256
ISBN-13: 9814522031
DOWNLOAD EBOOK →The aim of the conference was to find common elements between quantization and coherent states, and quantization on Poisson manifolds. Topics included are coherent states, geometric quantization, phase space quantization, deformation and *-products and Berry's phase.
Author: Jean-Pierre Gazeau
Publisher: Wiley-VCH
Published: 2009-09-03
Total Pages: 384
ISBN-13: 3527628290
DOWNLOAD EBOOK →This self-contained introduction discusses the evolution of the notion of coherent states, from the early works of Schrödinger to the most recent advances, including signal analysis. An integrated and modern approach to the utility of coherent states in many different branches of physics, it strikes a balance between mathematical and physical descriptions. Split into two parts, the first introduces readers to the most familiar coherent states, their origin, their construction, and their application and relevance to various selected domains of physics. Part II, mostly based on recent original results, is devoted to the question of quantization of various sets through coherent states, and shows the link to procedures in signal analysis.
Author: Syed Twareque Ali
Publisher: World Scientific Publishing Company Incorporated
Published: 1993-01-01
Total Pages: 244
ISBN-13: 9789810214470
DOWNLOAD EBOOK →Author: J-P Antoine
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 289
ISBN-13: 1489910603
DOWNLOAD EBOOK →The XIIIth Bialowieza Summer Workshop was held from July 9 to 15, 1994. While still within the general framework of Differential Geometric Methods in Physics, the XnIth Workshop was expanded in scope to include quantum groups, q-deformations and non-commutative geometry. It is expected that lectures on these topics will now become an integral part of future workshops. In the more traditional areas, lectures were devoted to topics in quantization, field theory, group representations, coherent states, complex and Poisson structures, the Berry phase, graded contractions and some infinite-dimensional systems. Those of us who have taken part in the evolution of the workshops over the years, feel a good measure of satisfaction with the excellent quality of the papers presented, in particular the mathematical rigour and novelty. Each year a significant number of new results are presented and future directions of research are discussed. Their freshness and immediacy inevitably leads to intense discussions and an exchange of ideas in an informal and physically charming environment. The present workshop also had a higher attendance than its predecessors, with ap proximately 65 registered participants. As usual, there was a large number of graduate students and young researchers among them.
Author: Didier Robert
Publisher: Springer Nature
Published: 2021-05-25
Total Pages: 577
ISBN-13: 3030708454
DOWNLOAD EBOOK →This second edition of the outstanding monograph on coherent states by Combescure and Robert published in 2012 is enriched with figures, historical information and numerical simulations and enlarged with five new chapters presenting important rigorous results obtained in the recent years. The new chapters include various applications such as to the time dependent Schroedinger equation and the Ehrenfest time, to the growth of norms and energy exchanges, to chaotic systems and classical systems with quantum ergodic behavior, and to open quantum systems, and to adiabatic decoupling for multicomponent systems Overall, this book presents the various types of coherent states introduced and studied in the physics and mathematics literature and describes their properties together with application to quantum physics problems. It is intended to serve as a compendium on coherent states and their applications for physicists and mathematicians, stretching from the basic mathematical structures of generalized coherent states in the sense of Perelomov via the semiclassical evolution of coherent states to various specific examples of coherent states (hydrogen atom, quantum oscillator, etc.). It goes beyond existing books on coherent states in terms of a rigorous mathematical framework
Author: D H Feng
Publisher: World Scientific
Published: 1994-05-26
Total Pages: 600
ISBN-13: 9814602515
DOWNLOAD EBOOK →The book consists of lectures delivered at the International Symposium on Coherent States: Past, Present, and Future, held in Oak Ridge, Tennessee, June 14 – 17 1993. Both theoretical and experimental subjects are treated. Theoretical subjects dealt with include quantum optics, quantum chaos, condensed matter physics, nuclear physics, high energy physics and foundational issues such as quantum-classical connections and various semiclassical quantization schemes. Experimental topics dealt with principally concern atomic and molecular physics and especially lasers. Topics related to coherent states, most notably wavelets, are also included. Contents: Quantum Versus Classical Phase in Optical Systems (G S Agarwal)Coherent States: How Far Can One Go? (J-P Antoine)Orthonormal Bases of Coherent States: The Canonical Case and the axGroup (I Daubechies)Dynamics of Coherent States as the Diffusion Process: Schrödinger's System, Bernstein Processes, and Quantum Evolution (P Garbaczewski)Some Reflections on Coherence and Ion Trapping (R J Glauber)Coherent States, Chaos, and Information (E J Heller & S Tomsovic)Coherent States as a Tool for Obtaining Rigorous Bounds (E H Lieb)Classical-Quantum Correspondence in Time-Dependent Perturbation Theory (S M McRae & E R Vrscay)Asymptotic Coherence of Gluons and of q-Bosons (C A Nelson)Electron Nuclear Dynamics with Coherent States (Y Öhrn & E Deumens)Quantum Coherent Operators (J P Solovej)Classicalization and Coherent States (W-M Zhang & D H Feng)Post-Banquet Talk (A S Wightman)and other papers Readership: Theoretical and applied physicists and mathematicians.
Author: Syed Twareque Ali
Publisher: Springer Science & Business Media
Published: 2013-10-30
Total Pages: 586
ISBN-13: 1461485355
DOWNLOAD EBOOK →This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. 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. The approach allows the user to take a classical-like view of quantum states in physics. 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; a further step allows one to dispense with the group context altogether. In this context, wavelets can be generated from coherent states of the affine group of the real line, and higher-dimensional wavelets arise from coherent states of other groups. The unified background makes transparent an entire range of properties of wavelets and coherent states. Many concrete examples, such as coherent states from semisimple Lie groups, Gazeau-Klauder coherent states, coherent states for the relativity groups, and several kinds of wavelets, are discussed in detail. The book concludes with a palette of potential applications, from the quantum physically oriented, like the quantum-classical transition or the construction of adequate states in quantum information, to the most innovative techniques to be used in data processing. Intended as an introduction to current research for graduate students and others entering the field, the mathematical discussion is self-contained. With its extensive references to the research literature, the first edition of the book is already a proven compendium for physicists and mathematicians active in the field, and with full coverage of the latest theory and results the revised second edition is even more valuable.
Author: Akira Inomata
Publisher: World Scientific
Published: 1992
Total Pages: 338
ISBN-13: 9789810206567
DOWNLOAD EBOOK →The authors examine several topical subjects, commencing with a general introduction to path integrals in quantum mechanics and the group theoretical backgrounds for path integrals. Applications of harmonic analysis, polar coordinate formulation, various techniques and path integrals on SU(2) and SU(1, 1) are discussed. Soluble examples presented include particle-flux system, a pulsed oscillator, magnetic monopole, the Coulomb problem in curved space and others.The second part deals with the SU(2) coherent states and their applications. Construction and generalization of the SU(2) coherent states, formulation of coherent path integrals for spin and unitary spin, and semiclassical quantization are presented. Applications are made to the study of quantum fluctuation, the nonlinear field model and phase holonomy.The final chapters present the theory of the SU(1, 1) coherent states and their applications. The radial coulomb problem, the Morse oscillator, and the large-N approximation are discussed. Applications to problems in quantum optics such as squeezed states, interaction with the squeezed vacuum states, and phase operator formalism are also included.This book will be useful as an introduction to the subject as well as a valuable work of reference.
Author: Jean-Pierre Antoine
Publisher: Springer
Published: 2018-06-01
Total Pages: 347
ISBN-13: 3319767321
DOWNLOAD EBOOK →Coherent states (CS) were originally introduced in 1926 by Schrödinger and rediscovered in the early 1960s in the context of laser physics. Since then, they have evolved into an extremely rich domain that pervades virtually every corner of physics, and have also given rise to a range of research topics in mathematics. The purpose of the 2016 CIRM conference was to bring together leading experts in the field with scientists interested in related topics, to jointly investigate their applications in physics, their various mathematical properties, and their generalizations in many directions. Instead of traditional proceedings, this book presents sixteen longer review-type contributions, which are the outcome of a collaborative effort by many conference participants, subsequently reviewed by independent experts. The book aptly illustrates the diversity of CS aspects, from purely mathematical topics to physical applications, including quantum gravity.
Author: Mark S Swanson
Publisher:
Published: 2020-08-07
Total Pages: 242
ISBN-13: 9780750335485
DOWNLOAD EBOOK →This book is a self-contained and concise introduction to the techniques and applications of path integral quantization and functional techniques, aimed at students and practitioners. The first half of the text focuses on quantum mechanics, including a review of the action formulation of classical mechanics and quantum mechanics in the Dirac operator and state formalism, and further examination of the path integral. The second part examines relativistic field theories, reviewing special relativity, as well as derivation of the path integral representation of the vacuum transition element for quantized scalar, spinor, and vector fields from the coherent state representation of the respective field theories. Key Features Concise introduction to the derivation and methods of path integral approaches to quantum mechanics and quantum field theory. Self-contained guide for students and practitioners
