Mathematical Quantization
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Mathematical Quantization
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Author : Nik Weaver
language : en
Publisher: CRC Press
Release Date : 2001-05-31
Mathematical Quantization written by Nik Weaver and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-31 with Mathematics categories.
With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of a
Quantization Pdes And Geometry
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Author : Dorothea Bahns
language : en
Publisher: Birkhäuser
Release Date : 2016-02-11
Quantization Pdes And Geometry written by Dorothea Bahns and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-11 with Mathematics categories.
This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability of solitary waves, and sub-Riemannian geometry. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen. The authors explain fundamental concepts and ideas and present them clearly. Starting from basic notions, these course notes take the reader to the point of current research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. All contributions are of interest to researchers in the respective fields, but they are also accessible to graduate students.
Mathematics Of Quantization And Quantum Fields
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Author : Jan Dereziński
language : en
Publisher: Cambridge University Press
Release Date : 2013-03-07
Mathematics Of Quantization And Quantum Fields written by Jan Dereziński and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Science categories.
A unique and definitive review of mathematical aspects of quantization and quantum field theory for graduate students and researchers.
Quantization Geometry And Noncommutative Structures In Mathematics And Physics
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Author : Alexander Cardona
language : en
Publisher: Springer
Release Date : 2017-10-26
Quantization Geometry And Noncommutative Structures In Mathematics And Physics written by Alexander Cardona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-26 with Science categories.
This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics.The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics.A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt.The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andruskiewitsch. The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved space-time, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to non-commutativity.An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the Batalin-Vilkovisky formalism and direct products of spectral triples.This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory.
Geometric Quantization
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Author : Nicholas Michael John Woodhouse
language : en
Publisher: Oxford University Press
Release Date : 1992
Geometric Quantization written by Nicholas Michael John Woodhouse and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
The geometric approach to quantization was introduced by Konstant and Souriau more than 20 years ago. It has given valuable and lasting insights into the relationship between classical and quantum systems, and continues to be a popular research topic. The ideas have proved useful in pure mathematics, notably in representation theory, as well as in theoretical physics. The most recent applications have been in conformal field theory and in the Jones-Witten theory of knots. The successful original edition of this book was published in 1980. Now it has been completely revised and extensively rewritten. The presentation has been simplified and many new examples have been added. The material on field theory has been expanded.
Arithmetic And Geometry Around Quantization
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Author : Özgür Ceyhan
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-12
Arithmetic And Geometry Around Quantization written by Özgür Ceyhan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-12 with Mathematics categories.
This volume comprises both research and survey articles originating from the conference on Arithmetic and Geometry around Quantization held in Istanbul in 2006. A wide range of topics related to quantization are covered, thus aiming to give a glimpse of a broad subject in very different perspectives.
Mathematical Aspects Of Quantization
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Author : Sam Evens
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Mathematical Aspects Of Quantization written by Sam Evens and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This book is a collection of expository articles from the Center of Mathematics at Notre Dame's 2011 program on quantization. Included are lecture notes from a summer school on quantization on topics such as the Cherednik algebra, geometric quantization, detailed proofs of Willwacher's results on the Kontsevich graph complex, and group-valued moment maps. This book also includes expository articles on quantization and automorphic forms, renormalization, Berezin-Toeplitz quantization in the complex setting, and the commutation of quantization with reduction, as well as an original article on derived Poisson brackets. The primary goal of this volume is to make topics in quantization more accessible to graduate students and researchers.
Mathematical Aspects Of Weyl Quantization And Phase
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Author : D A Dubin
language : en
Publisher: World Scientific
Release Date : 2000-06-12
Mathematical Aspects Of Weyl Quantization And Phase written by D A Dubin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-12 with Science categories.
This book analyzes in considerable generality the quantization–dequantization integral transform scheme of Weyl and Wigner, and considers several phase operator theories. It features: a thorough treatment of quantization in polar coordinates; dequantization by a new method of “motes”; a discussion of Moyal algebras; modifications of the transform method to accommodate operator orderings; a rigorous discussion of the Dicke laser model for one mode, fully quantum, in the thermodynamic limit; analysis of quantum phase theories based on the Toeplitz operator, the coherent state operator, the quantized phase space angle, and a sequence of finite rank operators. Contents:Fundamentals:BackgroundSome Remarks on Classical MechanicsThe Bounded ModelThe Smooth ModelRepresentations of the CCRProbability in Quantum MechanicsDynamical SystemsWeyl QuantizationQuantization and Phase:Quantization in Polar CoordinatesPhase OperatorsThe Laser ModelWeyl DequantizationThe Moyal ProductOrdered QuantizationAsymptoticsMeasurements Readership: Researchers in physics. Keywords:Weyl Quantization;Wigner Transform;Quantum Mechanics;Dequantization;Phase Operator;Angle Quantization;Laser Theory;Moyal Product;Measurement;Asymptotics;QuantizationReviews: “… it provides an excellent survey in a very broad sense of the present state-of-the-art in the subject as expressed in the book.” Mathematical Reviews “Many topics had not or had inadequately been treated in the literature so far, so that this book is the first satisfactory discussion of lasers and phase operators from the point of view of quantization theory … this excellent book can be strongly recommended to those interested in the application of abstract quantization theory to real physical systems.” Mathematics Abstracts
Born Jordan Quantization
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Author : Maurice A. de Gosson
language : en
Publisher: Springer
Release Date : 2016-01-11
Born Jordan Quantization written by Maurice A. de Gosson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-11 with Science categories.
This book presents a comprehensive mathematical study of the operators behind the Born–Jordan quantization scheme. The Schrödinger and Heisenberg pictures of quantum mechanics are equivalent only if the Born–Jordan scheme is used. Thus, Born–Jordan quantization provides the only physically consistent quantization scheme, as opposed to the Weyl quantization commonly used by physicists. In this book we develop Born–Jordan quantization from an operator-theoretical point of view, and analyze in depth the conceptual differences between the two schemes. We discuss various physically motivated approaches, in particular the Feynman-integral point of view. One important and intriguing feature of Born-Jordan quantization is that it is not one-to-one: there are infinitely many classical observables whose quantization is zero.
Deformation Quantization For Actions Of R D
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Author : Marc Aristide Rieffel
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Deformation Quantization For Actions Of R D written by Marc Aristide Rieffel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
This work describes a general construction of a deformation quantization for any Poisson bracket on a manifold which comes from an action of $R^d$ on that manifold. These deformation quantizations are strict, in the sense that the deformed product of any two functions is again a function and that there are corresponding involutions and operator norms. Many of the techniques involved are adapted from the theory of pseudo-differential operators. The construction is shown to have many favorable properties. A number of specific examples are described, ranging from basic ones such as quantum disks, quantum tori, and quantum spheres, to aspects of quantum groups.