Coherent states and their applications : a contemporary panorama /: a contemporary panorama. (2018)

• Record Type: Book
• Further Information: Note: Edited by Jean-Pierre Antoine, Fabio Bagarello, Jean-Pierre Gazeau.
• Editors: Antoine, Jean Pierre; Bagarello, Fabio, 1964-; Gazeau, Jean-Pierre
• Contents: 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. 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. 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). 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. 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.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource (xii, 347 pages), illustrations (some color)
• Subjects: 530.4; Physics; Coherent states; SCIENCE -- Energy; SCIENCE -- Mechanics -- General; SCIENCE -- Physics -- General; Coherent states; Physics; Mathematical Methods in Physics; Mathematical Applications in the Physical Sciences; Quantum Physics; Abstract Harmonic Analysis; Mathematics -- Applied; Science -- Quantum Theory; Mathematics -- Mathematical Analysis; Mathematical modelling; Quantum physics (quantum mechanics & quantum field theory); Complex analysis, complex variables; Mathematical physics; Quantum theory; Harmonic analysis; Science -- Mathematical Physics; Mathematical physics; Electronic books
• Languages: English
• ISBNs: 9783319767321; 3319767321
• Related ISBNs: 9783319767314; 3319767313
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed June 5, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.