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BL
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| Record Number
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865223
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| Title & Author
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Coherent states and their applications : : a contemporary panorama /\ edited by Jean-Pierre Antoine, Fabio Bagarello, Jean-Pierre Gazeau.
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| Publication Statement
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Cham, Switzerland :: Springer,, 2018.
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| Series Statement
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Springer proceedings in physics,; volume 205
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| Page. NO
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1 online resource (xii, 347 pages) :: illustrations (some color)
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| ISBN
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3030095681
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: 3319767321
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: 331976733X
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: 9783030095680
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: 9783319767321
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: 9783319767338
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3319767313
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9783319767314
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Intro; Preface; References; Contents; Contributors; 1 Enhanced Quantization: The Right way to Quantize Everything; 1.1 Introduction; 1.1.1 The Problem; 1.1.2 The Solution; 1.1.3 Discussion; 1.1.4 Some Physics; 1.2 Affine Variables; 1.2.1 Are Canonical Variables Available?; 1.2.2 A New Pair of Operators; 1.3 Spin Variables; 1.4 The Power of Enhanced Quantization; 1.4.1 Rotationally Symmetric Models; 1.4.2 Ultralocal Scalar Fields; 1.4.3 Covariant Scalar Field; 1.4.4 Affine Quantum Gravity; 1.5 Historical Note; References; 2 Square Integrable Representations, An Invaluable Tool.
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2.1 Introduction2.2 Coherent States and Square Integrable Representations; 2.2.1 Coherent States as a Tight Frame; 2.2.2 Square Integrable Representations in a Nutshell; 2.2.3 Further Remarks; 2.3 Square Integrable Representations of Semidirect Products; 2.4 Square Integrable Representations and Phase-Space Quantum Mechanics; 2.4.1 Quantization, Dequantization and Star Products; 2.4.2 Detour: Classical States and Functions of Positive Type; 2.4.3 Quantum States and Functions of Quantum Positive Type; 2.5 From a Mathematical Divertissement to Open Quantum Systems; 2.6 Conclusions; References.
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3 Coherent States for Compact Lie Groups and Their Large-N Limits3.1 Coherent States and Segal-Bargmann Transform for Lie Groups of Compact Type; 3.1.1 Lie Groups of Compact Type and Their Complexifications; 3.1.2 Heat Kernel; 3.1.3 Coherent States; 3.1.4 Resolution of the Identity; 3.1.5 Segal-Bargmann Transform; 3.2 Additional Results; 3.2.1 Geometric Quantization; 3.2.2 (1+1)-Dimensional Yang-Mills Theory; 3.2.3 Coherent States on Spheres; 3.2.4 Applications to Quantum Gravity; 3.3 The Large-N Limit; 3.3.1 Overview of Large-N Limit; 3.3.2 The Laplacian and Segal-Bargmann Transform on U(N).
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3.3.3 The Action of the Laplacian on Trace Polynomials3.3.4 Concentration Properties of the Heat Kernel Measures; 3.3.5 Summary; References; 4 Continuous Frames and the Kadison-Singer Problem; 4.1 From Pure States to Coherent States; 4.2 Lyapunov's Theorem for Continuous Frames; 4.3 Discrete Frames and Approximate Lyapunov's Theorem; 4.4 Scalable Frames and Discretization Problem; 4.5 Examples; References; 5 Coherence, Squeezing and Entanglement: An Example of Peaceful Coexistence; 5.1 Coherent States: A Smooth Introduction; 5.1.1 Standard Coherent States; 5.1.2 After 1963.
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5.1.3 Reproducing Kernel Hilbert Space: Instructional Material5.1.4 Horzela-Szafraniec's CSs and the Segal-Bargmann Transform; 5.1.5 The Measure: To Be or Not to Be?; 5.2 Holomorphic Hermite Polynomials; 5.2.1 Holomorphic Hermite Polynomials in a Single Variable; 5.2.2 Holomorphic Hermite Polynomials in Two Variables; 5.3 HSz CSs: Holomorphic Hermite Polynomials Perspective; 5.4 CSs for Holomorphic Hermite Polynomials; 5.4.1 Single Particle Hermite CSs: Coherence and Squeezing; 5.4.2 Bipartite CSs-Coherence, Squeezing and Entanglement; References; 6 Coherent State Maps for Kummer Shapes.
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| Abstract
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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.
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| Subject
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Coherent states.
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Coherent states.
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Complex analysis, complex variables.
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Mathematical modelling.
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Mathematical physics.
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Quantum physics (quantum mechanics quantum field theory)
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SCIENCE-- Energy.
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SCIENCE-- Mechanics-- General.
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SCIENCE-- Physics-- General.
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| Dewey Classification
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530.4
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| LC Classification
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QC6.4.C56
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| Added Entry
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Antoine, Jean Pierre
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Bagarello, Fabio,1964-
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Gazeau, Jean-Pierre
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