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000843361 24500 $$aCoherent states and their applications :$$ba contemporary panorama /$$cedited by Jean-Pierre Antoine, Fabio Bagarello, Jean-Pierre Gazeau.
000843361 264_1 $$aCham, Switzerland :$$bSpringer,$$c2018.
000843361 300__ $$a1 online resource (xii, 347 pages) :$$billustrations.
000843361 336__ $$atext$$btxt$$2rdacontent
000843361 337__ $$acomputer$$bc$$2rdamedia
000843361 338__ $$aonline resource$$bcr$$2rdacarrier
000843361 347__ $$atext file$$bPDF$$2rda
000843361 4901_ $$aSpringer proceedings in physics,$$x0930-8989 ;$$vvolume 205
000843361 504__ $$aIncludes bibliographical references and index.
000843361 5050_ $$aIntro; Preface; References; Contents; Contributors; 1 Enhanced Quantization: The Right way to Quantize Everything; 1.1 Introduction; 1.1.1 The Problem; 1.1.2 The Solution; 1.1.3 Discussion; 1.1.4 Some Physics; 1.2 Affine Variables; 1.2.1 Are Canonical Variables Available?; 1.2.2 A New Pair of Operators; 1.3 Spin Variables; 1.4 The Power of Enhanced Quantization; 1.4.1 Rotationally Symmetric Models; 1.4.2 Ultralocal Scalar Fields; 1.4.3 Covariant Scalar Field; 1.4.4 Affine Quantum Gravity; 1.5 Historical Note; References; 2 Square Integrable Representations, An Invaluable Tool
000843361 5058_ $$a2.1 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
000843361 5058_ $$a3 Coherent States for Compact Lie Groups and Their Large-N Limits3.1 Coherent States and Segal-Bargmann Transform for Lie Groups of Compact Type; 3.1.1 Lie Groups of Compact Type and Their Complexifications; 3.1.2 Heat Kernel; 3.1.3 Coherent States; 3.1.4 Resolution of the Identity; 3.1.5 Segal-Bargmann Transform; 3.2 Additional Results; 3.2.1 Geometric Quantization; 3.2.2 (1+1)-Dimensional Yang-Mills Theory; 3.2.3 Coherent States on Spheres; 3.2.4 Applications to Quantum Gravity; 3.3 The Large-N Limit; 3.3.1 Overview of Large-N Limit; 3.3.2 The Laplacian and Segal-Bargmann Transform on U(N)
000843361 5058_ $$a3.3.3 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
000843361 5058_ $$a5.1.3 Reproducing Kernel Hilbert Space: Instructional Material5.1.4 Horzela-Szafraniec's CSs and the Segal-Bargmann Transform; 5.1.5 The Measure: To Be or Not to Be?; 5.2 Holomorphic Hermite Polynomials; 5.2.1 Holomorphic Hermite Polynomials in a Single Variable; 5.2.2 Holomorphic Hermite Polynomials in Two Variables; 5.3 HSz CSs: Holomorphic Hermite Polynomials Perspective; 5.4 CSs for Holomorphic Hermite Polynomials; 5.4.1 Single Particle Hermite CSs: Coherence and Squeezing; 5.4.2 Bipartite CSs-Coherence, Squeezing and Entanglement; References; 6 Coherent State Maps for Kummer Shapes
000843361 506__ $$aAccess limited to authorized users.
000843361 520__ $$aCoherent states (CS) were originally introduced in 1926 by Schrödinger and rediscovered in the early 1960s in the context of laser physics. Since then, they have evolved into an extremely rich domain that pervades virtually every corner of physics, and have also given rise to a range of research topics in mathematics. The purpose of the 2016 CIRM conference was to bring together leading experts in the field with scientists interested in related topics, to jointly investigate their applications in physics, their various mathematical properties, and their generalizations in many directions. Instead of traditional proceedings, this book presents sixteen longer review-type contributions, which are the outcome of a collaborative effort by many conference participants, subsequently reviewed by independent experts. The book aptly illustrates the diversity of CS aspects, from purely mathematical topics to physical applications, including quantum gravity.
000843361 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed June 5, 2018).
000843361 650_0 $$aCoherent states.
000843361 7001_ $$aAntoine, Jean Pierre,$$eeditor.
000843361 7001_ $$aBagarello, Fabio,$$d1964-$$eeditor.
000843361 7001_ $$aGazeau, Jean-Pierre,$$eeditor.
000843361 77608 $$iPrint version: $$z3319767313$$z9783319767314$$w(OCoLC)1022085177
000843361 830_0 $$aSpringer proceedings in physics ;$$vv. 205.
000843361 852__ $$bebk
000843361 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-76732-1$$zOnline Access$$91397441.1
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