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.
Download or read book Coherent Transform Quantization and Poisson Geometry written by Mikhail Vladimirovich Karasev and published by American Mathematical Soc.. This book was released on 1998 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume copntains three extensive articles written by Karasev and his pupils. Topics covered include the following: coherent states and irreducible representations for algebras with non-Lie permutation relations, Hamilton dynamics and quantization over stable isotropic submanifolds, and infinitesimal tensor complexes over degenerate symplectic leaves in Poisson manifolds. The articles contain many examples (including from physics) and complete proofs.
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.
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.
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.
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
Download or read book Selected Papers from the 16th International Conference on Squeezed States and Uncertainty Relations ICSSUR 2019 written by Margarita A. Man’ko and published by MDPI. This book was released on 2020-11-09 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first quantum revolution started in the early 20th century and gave us new rules that govern physical reality. Accordingly, many devices that changed dramatically our lifestyle, such as transistors, medical scanners and lasers, appeared in the market. This was the origin of quantum technology, which allows us to organize and control the components of a complex system governed by the laws of quantum physics. This is in sharp contrast to conventional technology, which can only be understood within the framework of classical mechanics. We are now in the middle of a second quantum revolution. Although quantum mechanics is nowadays a mature discipline, quantum engineering as a technology is now emerging in its own right. We are about to manipulate and sense individual particles, measuring and exploiting their quantum properties. This is bringing major technical advances in many different areas, including computing, sensors, simulations, cryptography and telecommunications. The present collection of selected papers is a clear demonstration of the tremendous vitality of the field. The issue is composed of contributions from world leading researchers in quantum optics and quantum information, and presents viewpoints, both theoretical and experimental, on a variety of modern problems.
Download or read book Coherent Quantum Physics written by Arnold Neumaier and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-10-21 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces mathematicians, physicists, and philosophers to a new, coherent approach to theory and interpretation of quantum physics, in which classical and quantum thinking live peacefully side by side and jointly fertilize the intuition. The formal, mathematical core of quantum physics is cleanly separated from the interpretation issues. The book demonstrates that the universe can be rationally and objectively understood from the smallest to the largest levels of modeling. The thermal interpretation featured in this book succeeds without any change in the theory. It involves one radical step, the reinterpretation of an assumption that was virtually never questioned before - the traditional eigenvalue link between theory and observation is replaced by a q-expectation link: Objective properties are given by q-expectations of products of quantum fields and what is computable from these. Averaging over macroscopic spacetime regions produces macroscopic quantities with negligible uncertainty, and leads to classical physics. - Reflects the actual practice of quantum physics. - Models the quantum-classical interface through coherent spaces. - Interprets both quantum mechanics and quantum field theory. - Eliminates probability and measurement from the foundations. - Proposes a novel solution of the measurement problem.
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.
Download or read book Structural Aspects Of Quantum Field Theory In 2 Volumes written by Gerhard Grensing and published by World Scientific. This book was released on 2013-05-21 with total page 1596 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The book is primarily addressed to physicists. Nevertheless, as numerous examples are known in which exploration of the land where physics and mathematics overlap (and which quantum field theory definitely belongs to) resulted in important developments in mathematics, many mathematicians may also find this book interesting and even inspiring.'MathSciNetThis book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.The first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a rather detailed investigation of the fractional quantum Hall effect, and gives a stringent derivation of Laughlin's trial ground state wave function as an exact ground state.The second volume covers more advanced themes. In particular Connes' noncommutative geometry is dealt with in some considerable detail; the presentation attempts to acquaint the physics community with the substantial achievements that have been reached by means of this approach towards the understanding of the elusive Higgs particle. The book also covers the subject of quantum groups and its application to the fractional quantum Hall effect, as it is for this paradigmatic physical system that noncommutative geometry and quantum groups can be brought together.
Download or read book Journal of Physics A Mathematical and General written by INSTITUTE OF PHYSICS. (Great Britain). AMERICAN INSTITUTE OF PHYSICS. (USA) and published by . This book was released on 2002 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
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.
Download or read book Quantum Geometry Matrix Theory and Gravity written by Harold C. Steinacker and published by Cambridge University Press. This book was released on 2024-04-11 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on mathematical structures familiar from quantum mechanics, this book provides an introduction to quantization in a broad context before developing a framework for quantum geometry in Matrix Theory and string theory. Taking a physics-oriented approach to quantum geometry, this framework helps explain the physics of Yang–Mills-type matrix models, leading to a quantum theory of space-time and matter. This novel framework is then applied to Matrix Theory, which is defined through distinguished maximally supersymmetric matrix models related to string theory. A mechanism for gravity is discussed in depth, which emerges as a quantum effect on quantum space-time within Matrix Theory. Using explicit examples and exercises, readers will develop a physical intuition for the mathematical concepts and mechanisms. It will benefit advanced students and researchers in theoretical and mathematical physics, and is a useful resource for physicists and mathematicians interested in the geometrical aspects of quantization in a broader context.
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
Download or read book Nuclear Structure with Coherent States written by Apolodor Aristotel Raduta and published by Springer. This book was released on 2015-02-11 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the essential features of a large variety of nuclear structure properties, both collective and microscopic in nature. Most of results are given in an analytical form thus giving deep insight into the relevant phenomena. Using coherent states as variational states, which allows a description in the classical phase space, or provides the generating function for a boson basis, is an efficient tool to account, in a realistic fashion, for many complex properties. A detailed comparison with all existing nuclear structure models provides readers with a proper framework and, at the same time, demonstrates the prospects for new developments. The topics addressed are very much of current concern in the field. The book will appeal to practicing researchers and, due to its self-contained account, can also be successfully read and used by new graduate students.
