Quantization Coherent States And Poisson Structures

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Quantization, Coherent States, and Complex Structures

Author : J-P Antoine
Publisher : Springer Science & Business Media
ISBN 13 : 1489910603
Total Pages : 289 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Quantization, Coherent States, and Complex Structures by : J-P Antoine

Download or read book Quantization, Coherent States, and Complex Structures written by J-P Antoine and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantization And Coherent States Methods - Proceedings Of Xi Workshop On Geometric Methods In Physics

Author : S Twareque Ali
Publisher : World Scientific
ISBN 13 : 9814522031
Total Pages : 256 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Quantization And Coherent States Methods - Proceedings Of Xi Workshop On Geometric Methods In Physics by : S Twareque Ali

Download or read book Quantization And Coherent States Methods - Proceedings Of Xi Workshop On Geometric Methods In Physics written by S Twareque Ali and published by World Scientific. This book was released on 1993-10-29 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantization and Infinite-Dimensional Systems

Author : S.T. Ali
Publisher : Springer Science & Business Media
ISBN 13 : 1461525640
Total Pages : 273 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Quantization and Infinite-Dimensional Systems by : S.T. Ali

Download or read book Quantization and Infinite-Dimensional Systems written by S.T. Ali and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: As all participants know by now, the Bialowieza Summer Workshop has acquired a life of its own. The charming venue of the meetings, the informal atmosphere, the enthusiasm of the participants and the intensity of the scientific interaction have all conspired to make these meetings wonderful learning experiences. The XIIth Workshop (held from July 1 - 7, 1993) was once again a topical meeting within the general area of Differential Geometric Methods in Physics, focusing specifically on Quantization and Infinite-dimensional Systems. Altogether, about fifty participants attended the workshop. As before, the aim of the workshop was to have a small number of in-depth lectures on the main theme and a somewhat larger number of short presentations on related areas, while leaving enough free time for private discussions and exchange of ideas. Topics treated in the workshop included field theory, geometric quantization and symplectic geometry, coherent states methods, holomorphic representation theory, Poisson structures, non-commutative geometry, supersymmetry and quantum groups. The editors have the pleasant task of first thanking all the local organizers, in particular Dr. K. Gilewicz, for their painstaking efforts in ensuring the smooth running of the meeting and for organizing a delightful array of social events. Secondly, they would like to record their indebtedness to all the people who have contributed to this volume and to the redoubtable Ms. Cindy Parkinson without whose patient typesetting and editing skills the volume could hardly have seen the light of the day.

The Breadth of Symplectic and Poisson Geometry

Author : Jerrold E. Marsden
Publisher : Springer Science & Business Media
ISBN 13 : 0817644199
Total Pages : 666 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis The Breadth of Symplectic and Poisson Geometry by : Jerrold E. Marsden

Download or read book The Breadth of Symplectic and Poisson Geometry written by Jerrold E. Marsden and published by Springer Science & Business Media. This book was released on 2007-07-03 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: * The invited papers in this volume are written in honor of Alan Weinstein, one of the world’s foremost geometers * Contributions cover a broad range of topics in symplectic and differential geometry, Lie theory, mechanics, and related fields * Intended for graduate students and working mathematicians, this text is a distillation of prominent research and an indication of future trends in geometry, mechanics, and mathematical physics

Quantization, Geometry and Noncommutative Structures in Mathematics and Physics

Author : Alexander Cardona
Publisher : Springer
ISBN 13 : 3319654276
Total Pages : 347 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Quantization, Geometry and Noncommutative Structures in Mathematics and Physics by : Alexander Cardona

Download or read book Quantization, Geometry and Noncommutative Structures in Mathematics and Physics written by Alexander Cardona and published by Springer. This book was released on 2017-10-26 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Aspects of Quantization

Author : Sam Evens
Publisher : American Mathematical Soc.
ISBN 13 : 0821875736
Total Pages : 321 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mathematical Aspects of Quantization by : Sam Evens

Download or read book Mathematical Aspects of Quantization written by Sam Evens and published by American Mathematical Soc.. This book was released on 2012 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantization by Coherent States

Author : Michael Clifford Ashworth
Publisher :
ISBN 13 :
Total Pages : 312 pages
Book Rating : 4.:/5 (56 download)

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Book Synopsis Quantization by Coherent States by : Michael Clifford Ashworth

Download or read book Quantization by Coherent States written by Michael Clifford Ashworth and published by . This book was released on 1997 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quantization of Singular Symplectic Quotients

Author : N.P. Landsman
Publisher : Birkhäuser
ISBN 13 : 3034883641
Total Pages : 360 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Quantization of Singular Symplectic Quotients by : N.P. Landsman

Download or read book Quantization of Singular Symplectic Quotients written by N.P. Landsman and published by Birkhäuser. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first exposition of the quantization theory of singular symplectic (Marsden-Weinstein) quotients and their applications to physics. The reader will acquire an introduction to the various techniques used in this area, as well as an overview of the latest research approaches. These involve classical differential and algebraic geometry, as well as operator algebras and noncommutative geometry. Thus one will be amply prepared to follow future developments in this field.

Quantum Algebras and Poisson Geometry in Mathematical Physics

Author : Mikhail Vladimirovich Karasev
Publisher : American Mathematical Soc.
ISBN 13 : 9780821840405
Total Pages : 296 pages
Book Rating : 4.8/5 (44 download)

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Book Synopsis Quantum Algebras and Poisson Geometry in Mathematical Physics by : Mikhail Vladimirovich Karasev

Download or read book Quantum Algebras and Poisson Geometry in Mathematical Physics written by Mikhail Vladimirovich Karasev and published by American Mathematical Soc.. This book was released on 2005 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents applications of Poisson geometry to some fundamental well-known problems in mathematical physics. This volume is suitable for graduate students and researchers interested in mathematical physics. It uses methods such as: unexpected algebras with non-Lie commutation relations, dynamical systems theory, and semiclassical asymptotics.

From Geometry to Quantum Mechanics

Author : Yoshiaki Maeda
Publisher : Springer Science & Business Media
ISBN 13 : 0817645306
Total Pages : 326 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis From Geometry to Quantum Mechanics by : Yoshiaki Maeda

Download or read book From Geometry to Quantum Mechanics written by Yoshiaki Maeda and published by Springer Science & Business Media. This book was released on 2007-04-22 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Invited articles in differential geometry and mathematical physics in honor of Hideki Omori * Focus on recent trends and future directions in symplectic and Poisson geometry, global analysis, Lie group theory, quantizations and noncommutative geometry, as well as applications of PDEs and variational methods to geometry * Will appeal to graduate students in mathematics and quantum mechanics; also a reference

An Introduction to Noncommutative Geometry

Author : Joseph C. Várilly
Publisher : European Mathematical Society
ISBN 13 : 9783037190241
Total Pages : 134 pages
Book Rating : 4.1/5 (92 download)

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Book Synopsis An Introduction to Noncommutative Geometry by : Joseph C. Várilly

Download or read book An Introduction to Noncommutative Geometry written by Joseph C. Várilly and published by European Mathematical Society. This book was released on 2006 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative geometry, inspired by quantum physics, describes singular spaces by their noncommutative coordinate algebras and metric structures by Dirac-like operators. Such metric geometries are described mathematically by Connes' theory of spectral triples. These lectures, delivered at an EMS Summer School on noncommutative geometry and its applications, provide an overview of spectral triples based on examples. This introduction is aimed at graduate students of both mathematics and theoretical physics. It deals with Dirac operators on spin manifolds, noncommutative tori, Moyal quantization and tangent groupoids, action functionals, and isospectral deformations. The structural framework is the concept of a noncommutative spin geometry; the conditions on spectral triples which determine this concept are developed in detail. The emphasis throughout is on gaining understanding by computing the details of specific examples. The book provides a middle ground between a comprehensive text and a narrowly focused research monograph. It is intended for self-study, enabling the reader to gain access to the essentials of noncommutative geometry. New features since the original course are an expanded bibliography and a survey of more recent examples and applications of spectral triples.

Geometric Methods in Physics

Author : Piotr Kielanowski
Publisher : Springer Science & Business Media
ISBN 13 : 3034804482
Total Pages : 431 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Geometric Methods in Physics by : Piotr Kielanowski

Download or read book Geometric Methods in Physics written by Piotr Kielanowski and published by Springer Science & Business Media. This book was released on 2012-11-05 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Białowieża workshops on Geometric Methods in Physics are among the most important meetings in the field. Every year some 80 to 100 participants from both mathematics and physics join to discuss new developments and to interchange ideas. This volume contains contributions by selected speakers at the XXX meeting in 2011 as well as additional review articles and shows that the workshop remains at the cutting edge of ongoing research. The 2011 workshop focussed on the works of the late Felix A. Berezin (1931–1980) on the occasion of his 80th anniversary as well as on Bogdan Mielnik and Stanisław Lech Woronowicz on their 75th and 70th birthday, respectively. The groundbreaking work of Berezin is discussed from today’s perspective by presenting an overview of his ideas and their impact on further developments. He was, among other fields, active in representation theory, general concepts of quantization and coherent states, supersymmetry and supermanifolds. Another focus lies on the accomplishments of Bogdan Mielnik and Stanisław Lech Woronowicz. Mielnik’s geometric approach to the description of quantum mixed states, the method of quantum state manipulation and their important implications for quantum computing and quantum entanglement are discussed as well as the intricacies of the quantum time operator. Woronowicz’ fruitful notion of a compact quantum group and related topics are also addressed.

Long Time Behaviour of Classical and Quantum Systems

Author : Sandro Graffi
Publisher : World Scientific
ISBN 13 : 9789812794598
Total Pages : 320 pages
Book Rating : 4.7/5 (945 download)

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Book Synopsis Long Time Behaviour of Classical and Quantum Systems by : Sandro Graffi

Download or read book Long Time Behaviour of Classical and Quantum Systems written by Sandro Graffi and published by World Scientific. This book was released on 2001 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Return to equilibrium in classical and quantum systems / Carlangelo Liverani -- Quantum resonances and trapped trajectories / Johannes Sjostrand -- Return to thermal equilibrium in quantum statistical mechanics / Volker Bach -- Small oscillations in some nonlinear PDE's / Dario Bambusi and Simone Paleari -- The semi-classical Van-Vleck Formula. Application to the Aharonov-Bohm effect / Jean-Marie Bily and Didier Robert -- Fractal dimensions and quantum evolution associated with sparse potential Jacobi matrices / Jean-Michel Combes and Giorgio Mantica -- Infinite step billiards / Mirko Degli Esposti -- Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator / Bernard Helffer and Thierry Ramond -- Asymptotics of scattering poles for two strictly convex obstacles / Mitsuru Ikawa -- Parabolic dynamical systems and inducing / Stefano Isola -- QFT for scalar particles in external fields on Riemannian manifolds / Hiroshi Isozaki -- Existence and born-Oppenheimer Asymptotics of the total scattering cross-section in ion-atom collisions / Thierry Jecko, Markus Klein and Xue Ping Wang -- On asymptotic perturbation theory for quantum mechanics / Gheorghe Nenciu -- Destruction of the beating effect in a periodically driven double-well / Andrea Sacchetti -- Berezin-Toeplitz quantization and Berezin transform / Martin Schlichenmaier.

Long Time Behaviour Of Classical And Quantum Systems - Proceedings Of The Bologna Aptex International Conference

Author : Sandro Graffi
Publisher : World Scientific
ISBN 13 : 9814491535
Total Pages : 299 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Long Time Behaviour Of Classical And Quantum Systems - Proceedings Of The Bologna Aptex International Conference by : Sandro Graffi

Download or read book Long Time Behaviour Of Classical And Quantum Systems - Proceedings Of The Bologna Aptex International Conference written by Sandro Graffi and published by World Scientific. This book was released on 2001-04-02 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is centered on the two minicourses conducted by C Liverani (Rome) and J Sjoestrand (Paris) on the return to equilibrium in classical statistical mechanics and the location of quantum resonances via semiclassical analysis, respectively. The other contributions cover related topics of classical and quantum mechanics, such as scattering theory, classical and quantum statistical mechanics, dynamical localization, quantum chaos, ergodic theory and KAM techniques.

Philosophy of Physics

Author : Jeremy Butterfield
Publisher : Elsevier
ISBN 13 : 0444515607
Total Pages : 1481 pages
Book Rating : 4.4/5 (445 download)

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Book Synopsis Philosophy of Physics by : Jeremy Butterfield

Download or read book Philosophy of Physics written by Jeremy Butterfield and published by Elsevier. This book was released on 2007 with total page 1481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ambition of this volume is twofold: to provide a comprehensive overview of the field and to serve as an indispensable reference work for anyone who wants to work in it. For example, any philosopher who hopes to make a contribution to the topic of the classical-quantum correspondence will have to begin by consulting Klaas Landsman's chapter. The organization of this volume, as well as the choice of topics, is based on the conviction that the important problems in the philosophy of physics arise from studying the foundations of the fundamental theories of physics. It follows that there is no sharp line to be drawn between philosophy of physics and physics itself. Some of the best work in the philosophy of physics is being done by physicists, as witnessed by the fact that several of the contributors to the volume are theoretical physicists: viz., Ellis, Emch, Harvey, Landsman, Rovelli, 't Hooft, the last of whom is a Nobel laureate. Key features - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences that have grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers

Mathematical Topics Between Classical and Quantum Mechanics

Author : Nicholas P. Landsman
Publisher : Springer Science & Business Media
ISBN 13 : 146121680X
Total Pages : 547 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Mathematical Topics Between Classical and Quantum Mechanics by : Nicholas P. Landsman

Download or read book Mathematical Topics Between Classical and Quantum Mechanics written by Nicholas P. Landsman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph draws on two traditions: the algebraic formulation of quantum mechanics as well as quantum field theory, and the geometric theory of classical mechanics. These are combined in a unified treatment of the theory of Poisson algebras of observables and pure state spaces with a transition probability, which leads on to a discussion of the theory of quantization and the classical limit from this perspective. A prototype of quantization comes from the analogy between the C*- algebra of a Lie groupoid and the Poisson algebra of the corresponding Lie algebroid. The parallel between reduction of symplectic manifolds in classical mechanics and induced representations of groups and C*- algebras in quantum mechanics plays an equally important role. Examples from physics include constrained quantization, curved spaces, magnetic monopoles, gauge theories, massless particles, and $theta$- vacua. Accessible to mathematicians with some prior knowledge of classical and quantum mechanics, and to mathematical physicists and theoretical physicists with some background in functional analysis.

Twenty Years of Bialowieza

Author : Syed Twareque Ali
Publisher : World Scientific
ISBN 13 : 9812701249
Total Pages : 275 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Twenty Years of Bialowieza by : Syed Twareque Ali

Download or read book Twenty Years of Bialowieza written by Syed Twareque Ali and published by World Scientific. This book was released on 2005 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume marks the twentieth anniversary of the Bialowieza series of meetings on Differential Geometric Methods in Physics; the anniversary meeting was held during July 1OCo7, 2001. The Bialowieza meetings, held every year during the first week of July, have now grown into an annual pilgrimage for an international group of physicists and mathematicians. The topics discussed at the meetings, while within the broad area of differential geometric methods in physics, have focused around quantization, coherent states, infinite dimensional systems, symplectic geometry, spectral theory and harmonic analysis. The present volume brings together a set of specially invited papers from leading experts in the various fields, who have contributed to these meetings and whose work represents a cross-section of the topics discussed. Consequently, rather than a proceedings volume, this book embodies the spirit of the Bialowieza workshops and reflects their scientific tenor, as a tribute to the completion of two decades of a shared scientific experience. This book will be of interest to researchers and graduate students working in the area of differential geometric methods in physics, as it gives interesting glimpses into the present state of the art from different points of view."