Geometric Quantization In Action

Author : N.E. Hurt
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400969636

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Geometric Quantization in Action by N.E. Hurt Pdf

Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem. one day, perhaps you will fmd the final question. G. K. Chesterton, The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geo metry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical progmmming profit from homotopy theory; Lie algebras are relevant to fIltering; and prediction and electrical engineering can use Stein spaces.

Author : N.E. Hurt
Publisher : Springer
Page : 356 pages
File Size : 53,6 Mb
Release : 1982-12-31
Category : Mathematics
ISBN : 9027714266

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Geometric Quantization in Action by N.E. Hurt Pdf

Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem. one day, perhaps you will fmd the final question. G. K. Chesterton, The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geo metry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical progmmming profit from homotopy theory; Lie algebras are relevant to fIltering; and prediction and electrical engineering can use Stein spaces.

Author : S Twareque Ali,Anatol Odzijewicz,I M Mladenov
Publisher : World Scientific
Page : 256 pages
File Size : 44,7 Mb
Release : 1993-10-29
Category : Electronic
ISBN : 9789814522038

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Quantization And Coherent States Methods - Proceedings Of Xi Workshop On Geometric Methods In Physics by S Twareque Ali,Anatol Odzijewicz,I M Mladenov Pdf

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.

Author : Nicholas Michael John Woodhouse
Publisher : Oxford University Press
Page : 324 pages
File Size : 51,5 Mb
Release : 1992
Category : Mathematics
ISBN : 0198502702

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Geometric Quantization by Nicholas Michael John Woodhouse Pdf

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.

Author : Jedrzej Sniatycki
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 42,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461260660

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Geometric Quantization and Quantum Mechanics by Jedrzej Sniatycki Pdf

This book contains a revised and expanded version of the lecture notes of two seminar series given during the academic year 1976/77 at the Department of Mathematics and Statistics of the University of Calgary, and in the summer of 1978 at the Institute of Theoretical Physics of the Technical University Clausthal. The aim of the seminars was to present geometric quantization from the point of view· of its applica tions to quantum mechanics, and to introduce the quantum dynamics of various physical systems as the result of the geometric quantization of the classical dynamics of these systems. The group representation aspects of geometric quantiza tion as well as proofs of the existence and the uniqueness of the introduced structures can be found in the expository papers of Blattner, Kostant, Sternberg and Wolf, and also in the references quoted in these papers. The books of Souriau (1970) and Simms and Woodhouse (1976) present the theory of geometric quantization and its relationship to quantum mech anics. The purpose of the present book is to complement the preceding ones by including new developments of the theory and emphasizing the computations leading to results in quantum mechanics.

Author : Yoshiaki Maeda,Hideki Omori,Alan Weinstein
Publisher : American Mathematical Soc.
Page : 285 pages
File Size : 47,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821803028

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Symplectic Geometry and Quantization by Yoshiaki Maeda,Hideki Omori,Alan Weinstein Pdf

This volume contains the refereed proceedings of two symposia on symplectic geometry and quantization problems which were held in Japan in July 1993. The purpose of the symposia was to discuss recent progress in a range of related topics in symplectic geometry and mathematical physics, including symplectic groupoids, geometric quantization, noncommutative differential geometry, equivariant cohomology, deformation quantization, topological quantum field theory, and knot invariants. The book provides insight into how these different topics relate to one another and offers intriguing new problems. Providing a look at the frontier of research in symplectic geometry and quantization, this book is suitable as a source book for a seminar in symplectic geometry.

Author : Sean Bates,Alan Weinstein
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 55,8 Mb
Release : 1997
Category : Mathematics
ISBN : 0821807986

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Lectures on the Geometry of Quantization by Sean Bates,Alan Weinstein Pdf

These notes are based on a course entitled ``Symplectic Geometry and Geometric Quantization'' taught by Alan Weinstein at the University of California, Berkeley (fall 1992) and at the Centre Emile Borel (spring 1994). The only prerequisite for the course needed is a knowledge of the basic notions from the theory of differentiable manifolds (differential forms, vector fields, transversality, etc.). The aim is to give students an introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role these ideas play in formalizing the transition between the mathematics of classical dynamics (hamiltonian flows on symplectic manifolds) and quantum mechanics (unitary flows on Hilbert spaces). These notes are meant to function as a guide to the literature. The authors refer to other sources for many details that are omitted and can be bypassed on a first reading.

Author : Mircea Puta
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401119924

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Hamiltonian Mechanical Systems and Geometric Quantization by Mircea Puta Pdf

This volume presents various aspects of the geometry of symplectic and Poisson manifolds, and applications in Hamiltonian mechanics and geometric quantization are indicated. Chapter 1 presents some general facts about symplectic vector space, symplectic manifolds and symplectic reduction. Chapter 2 deals with the study of Hamiltonian mechanics. Chapter 3 considers some standard facts concerning Lie groups and algebras which lead to the theory of momentum mappings and the Marsden--Weinstein reduction. Chapters 4 and 5 consider the theory and the stability of equilibrium solutions of Hamilton--Poisson mechanical systems. Chapters 6 and 7 are devoted to the theory of geometric quantization. This leads, in Chapter 8, to topics such as foliated cohomology, the theory of the Dolbeault--Kostant complex, and their applications. A discussion of the relation between geometric quantization and the Marsden--Weinstein reduction is presented in Chapter 9. The final chapter considers extending the theory of geometric quantization to Poisson manifolds, via the theory of symplectic groupoids. Each chapter concludes with problems and solutions, many of which present significant applications and, in some cases, major theorems. For graduate students and researchers whose interests and work involve symplectic geometry and Hamiltonian mechanics.

Author : P. Bandyopadhyay
Publisher : Springer Science & Business Media
Page : 236 pages
File Size : 43,9 Mb
Release : 2013-03-07
Category : Science
ISBN : 9789401154260

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Geometry, Topology and Quantization by P. Bandyopadhyay Pdf

This is a monograph on geometrical and topological features which arise in various quantization procedures. Quantization schemes consider the feasibility of arriving at a quantum system from a classical one and these involve three major procedures viz. i) geometric quantization, ii) Klauder quantization, and iii) stochastic quanti zation. In geometric quantization we have to incorporate a hermitian line bundle to effectively generate the quantum Hamiltonian operator from a classical Hamil tonian. Klauder quantization also takes into account the role of the connection one-form along with coordinate independence. In stochastic quantization as pro posed by Nelson, Schrodinger equation is derived from Brownian motion processes; however, we have difficulty in its relativistic generalization. It has been pointed out by several authors that this may be circumvented by formulating a new geometry where Brownian motion proceses are considered in external as well as in internal space and, when the complexified space-time is considered, the usual path integral formulation is achieved. When this internal space variable is considered as a direc tion vector introducing an anisotropy in the internal space, we have the quantization of a Fermi field. This helps us to formulate a stochastic phase space formalism when the internal extension can be treated as a gauge theoretic extension. This suggests that massive fermions may be considered as Skyrme solitons. The nonrelativistic quantum mechanics is achieved in the sharp point limit.

Author : David John Simms,Nicholas Michael John Woodhouse
Publisher : Springer
Page : 188 pages
File Size : 54,7 Mb
Release : 1976
Category : Science
ISBN : UOM:39015057383286

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Lectures on Geometric Quantization by David John Simms,Nicholas Michael John Woodhouse Pdf

Author : Özgür Ceyhan,Yu. I. Manin,Matilde Marcolli
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 48,8 Mb
Release : 2010-01-12
Category : Mathematics
ISBN : 9780817648312

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Arithmetic and Geometry Around Quantization by Özgür Ceyhan,Yu. I. Manin,Matilde Marcolli Pdf

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.

Author : Alexander Cardona,Pedro Morales,Hernán Ocampo,Sylvie Paycha,Andrés F. Reyes Lega
Publisher : Springer
Page : 341 pages
File Size : 55,9 Mb
Release : 2017-10-26
Category : Science
ISBN : 9783319654270

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Quantization, Geometry and Noncommutative Structures in Mathematics and Physics by Alexander Cardona,Pedro Morales,Hernán Ocampo,Sylvie Paycha,Andrés F. Reyes Lega Pdf

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.

Author : Ivailo M. Mladenov,Gregory L. Naber
Publisher : Unknown
Page : 308 pages
File Size : 53,9 Mb
Release : 2000
Category : Biomathematics
ISBN : UOM:39015054175313

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Geometry, Integrability and Quantization by Ivailo M. Mladenov,Gregory L. Naber Pdf

Author : Marc Aristide Rieffel
Publisher : American Mathematical Soc.
Page : 93 pages
File Size : 41,5 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825754

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Deformation Quantization for Actions of $R^d$ by Marc Aristide Rieffel Pdf

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.

Author : Chiara Esposito
Publisher : Springer
Page : 98 pages
File Size : 48,6 Mb
Release : 2014-09-04
Category : Science
ISBN : 9783319092904

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Formality Theory by Chiara Esposito Pdf

This book is a survey of the theory of formal deformation quantization of Poisson manifolds, in the formalism developed by Kontsevich. It is intended as an educational introduction for mathematical physicists who are dealing with the subject for the first time. The main topics covered are the theory of Poisson manifolds, star products and their classification, deformations of associative algebras and the formality theorem. Readers will also be familiarized with the relevant physical motivations underlying the purely mathematical construction.