Geometric Quantization In Action
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Geometric Quantization In Action
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Author : N.E. Hurt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Quantization In Action written by N.E. Hurt 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 2012-12-06 with Mathematics categories.
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.
Geometric Quantization In Action
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Author : N.E. Hurt
language : en
Publisher: Springer
Release Date : 1982-12-31
Geometric Quantization In Action written by N.E. Hurt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-12-31 with Mathematics categories.
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.
Quantization And Coherent States Methods Proceedings Of Xi Workshop On Geometric Methods In Physics
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Author : S Twareque Ali
language : en
Publisher: World Scientific
Release Date : 1993-10-29
Quantization And Coherent States Methods Proceedings Of Xi Workshop On Geometric Methods In Physics written by S Twareque Ali and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-29 with categories.
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.
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.
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.
Lectures On The Geometry Of Quantization
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Author : Sean Bates
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Lectures On The Geometry Of Quantization written by Sean Bates 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 1997 with Mathematics categories.
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.
Symplectic Geometry And Quantization
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Author : Yoshiaki Maeda
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Symplectic Geometry And Quantization written by Yoshiaki Maeda 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 1994 with Mathematics categories.
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.
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 And Quantum Mechanics
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Author : Jedrzej Sniatycki
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Quantization And Quantum Mechanics written by Jedrzej Sniatycki 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 2012-12-06 with Science categories.
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.
Moment Maps Cobordisms And Hamiltonian Group Actions
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Author : Victor Guillemin
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Moment Maps Cobordisms And Hamiltonian Group Actions written by Victor Guillemin 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 2002 with Cobordism theory categories.
During the last 20 years, ``localization'' has been one of the dominant themes in the area of equivariant differential geometry. Typical results are the Duistermaat-Heckman theory, the Berline-Vergne-Atiyah-Bott localization theorem in equivariant de Rham theory, and the ``quantization commutes with reduction'' theorem and its various corollaries. To formulate the idea that these theorems are all consequences of a single result involving equivariant cobordisms, the authors have developed a cobordism theory that allows the objects to be non-compact manifolds. A key ingredient in this non-compact cobordism is an equivariant-geometrical object which they call an ``abstract moment map''. This is a natural and important generalization of the notion of a moment map occurring in the theory of Hamiltonian dynamics. The book contains a number of appendices that include introductions to proper group-actions on manifolds, equivariant cohomology, Spin${^\mathrm{c}}$-structures, and stable complex structures. It is geared toward graduate students and research mathematicians interested in differential geometry. It is also suitable for topologists, Lie theorists, combinatorists, and theoretical physicists. Prerequisite is some expertise in calculus on manifolds and basic graduate-level differential geometry.