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Author : ÃzgÃ1⁄4r Ceyhan
Publisher :
ISBN 13 : 9780817648329
Total Pages : 302 pages
Book Rating : 4.6/5 (483 download)
Download or read book Arithmetic and Geometry Around Quantization written by ÃzgÃ1⁄4r Ceyhan and published by . This book was released on 2010-04-17 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Özgür Ceyhan
Publisher : Springer Science & Business Media
ISBN 13 : 0817648313
Total Pages : 292 pages
Book Rating : 4.8/5 (176 download)
Download or read book Arithmetic and Geometry Around Quantization written by Özgür Ceyhan and published by Springer Science & Business Media. This book was released on 2010-01-12 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Springer
ISBN 13 : 3319654276
Total Pages : 341 pages
Book Rating : 4.3/5 (196 download)
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 341 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.
Author : Sean Bates
Publisher : American Mathematical Soc.
ISBN 13 : 9780821807989
Total Pages : 150 pages
Book Rating : 4.8/5 (79 download)
Download or read book Lectures on the Geometry of Quantization written by Sean Bates and published by American Mathematical Soc.. This book was released on 1997 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Nik Weaver
Publisher : CRC Press
ISBN 13 : 1420036238
Total Pages : 296 pages
Book Rating : 4.4/5 (2 download)
Download or read book Mathematical Quantization written by Nik Weaver and published by CRC Press. This book was released on 2001-05-31 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 variety of topics. Detailed here for the first time, the fundamental idea of mathematical quantization is that sets are replaced by Hilbert spaces. Building on this idea, and most importantly on the fact that scalar-valued functions on a set correspond to operators on a Hilbert space, one can determine quantum analogs of a variety of classical structures. In particular, because topologies and measure classes on a set can be treated in terms of scalar-valued functions, we can transfer these constructions to the quantum realm, giving rise to C*- and von Neumann algebras. In the first half of the book, the author quickly builds the operator algebra setting. He uses this as a unifying theme in the second half, in which he treats several active research topics, some for the first time in book form. These include the quantum plane and tori, operator spaces, Hilbert modules, Lipschitz algebras, and quantum groups. For graduate students, Mathematical Quantization offers an ideal introduction to a research area of great current interest. For professionals in operator algebras and functional analysis, it provides a readable tour of the current state of the field.
Author : Nicholas Michael John Woodhouse
Publisher : Oxford University Press
ISBN 13 : 9780198502708
Total Pages : 324 pages
Book Rating : 4.5/5 (27 download)
Download or read book Geometric Quantization written by Nicholas Michael John Woodhouse and published by Oxford University Press. This book was released on 1992 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Marshall Harvey Stone
Publisher : American Mathematical Soc.
ISBN 13 : 0821834029
Total Pages : 422 pages
Book Rating : 4.8/5 (218 download)
Download or read book Operator Algebras, Quantization, and Noncommutative Geometry written by Marshall Harvey Stone and published by American Mathematical Soc.. This book was released on 2004 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: John von Neumann and Marshall Stone were two giants of Twentieth Century mathematics. In honor of the 100th anniversary of their births, a mathematical celebration was organized featuring developments in fields where both men were major influences. This volume contains articles from the AMS Special Session, Operator Algebras, Quantization and Noncommutative Geometry: A Centennial Celebration in Honor of John von Neumann and Marshall H. Stone.Papers range from expository and historical surveys to original research articles. All articles were carefully refereed and cover a broad range of mathematical topics reflecting the fundamental ideas of von Neumann and Stone. Most contributions are expanded versions of the talks and were written exclusively for this volume. Included, among others, are articles by George W. Mackey, Nigel Higson, and Marc Rieffel. Also featured is a reprint of P.R. Halmos' ""The Legend of John von Neumann"". The book is suitable for graduate students and researchers interested in operator algebras and applications, including noncommutative geometry.
Author : Jean-Luc Brylinski
Publisher : Springer Science & Business Media
ISBN 13 : 0817647309
Total Pages : 317 pages
Book Rating : 4.8/5 (176 download)
Download or read book Loop Spaces, Characteristic Classes and Geometric Quantization written by Jean-Luc Brylinski and published by Springer Science & Business Media. This book was released on 2007-11-15 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac’s quantization of the electrical charge.
Author : Sam Evens
Publisher : American Mathematical Soc.
ISBN 13 : 0821875736
Total Pages : 321 pages
Book Rating : 4.8/5 (218 download)
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.
Author : Yoshiaki Maeda
Publisher : American Mathematical Soc.
ISBN 13 : 0821803026
Total Pages : 285 pages
Book Rating : 4.8/5 (218 download)
Download or read book Symplectic Geometry and Quantization written by Yoshiaki Maeda and published by American Mathematical Soc.. This book was released on 1994 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Giuseppe Dito
Publisher : American Mathematical Soc.
ISBN 13 : 0821841475
Total Pages : 143 pages
Book Rating : 4.8/5 (218 download)
Download or read book Non-commutative Geometry in Mathematics and Physics written by Giuseppe Dito and published by American Mathematical Soc.. This book was released on 2008 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume represents the proceedings of the conference on Topics in Deformation Quantization and Non-Commutative Structures held in Mexico City in September 2005. It contains survey papers and original contributions by various experts in the fields of deformation quantization and non-commutative derived algebraic geometry in the interface between mathematics and physics. It also contains an article based on the XI Memorial Lectures given by M. Kontsevich, which were delivered as part of the conference. This is an excellent introductory volume for readers interested in learning about quantization as deformation, Hopf algebras, and Hodge structures in the framework of non-commutative algebraic geometry.
Author : Matilde Marcolli
Publisher : Springer Science & Business Media
ISBN 13 : 3834898317
Total Pages : 240 pages
Book Rating : 4.8/5 (348 download)
Download or read book Quantum Groups and Noncommutative Spaces written by Matilde Marcolli and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differential-geometric approaches. It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group symmetries. The volume collects surveys by experts which originate from an acitvity at the Max-Planck-Institute for Mathematics in Bonn.
Author : Ernst Binz
Publisher : American Mathematical Soc.
ISBN 13 : 0821844954
Total Pages : 321 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Geometry of Heisenberg Groups written by Ernst Binz and published by American Mathematical Soc.. This book was released on 2008 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The three-dimensional Heisenberg group, being a quite simple non-commutative Lie group, appears prominently in various applications of mathematics. The goal of this book is to present basic geometric and algebraic properties of the Heisenberg group and its relation to other important mathematical structures (the skew field of quaternions, symplectic structures, and representations) and to describe some of its applications. In particular, the authors address such subjects as signal analysis and processing, geometric optics, and quantization. In each case, the authors present necessary details of the applied topic being considered." "This book manages to encompass a large variety of topics being easily accessible in its fundamentals. It can be useful to students and researchers working in mathematics and in applied mathematics."--BOOK JACKET.
Author : Vladimir Fock
Publisher : Birkhäuser
ISBN 13 : 3319335782
Total Pages : 220 pages
Book Rating : 4.3/5 (193 download)
Download or read book Geometry and Quantization of Moduli Spaces written by Vladimir Fock and published by Birkhäuser. This book was released on 2016-12-25 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on four advanced courses held at the Centre de Recerca Matemàtica (CRM), Barcelona. It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces. The lectures focus on the geometry of moduli spaces which are mostly associated to compact Riemann surfaces, and are presented from both classical and quantum perspectives.
Author : N.E. Hurt
Publisher : Springer
ISBN 13 : 9789027714268
Total Pages : 356 pages
Book Rating : 4.7/5 (142 download)
Download or read book Geometric Quantization in Action written by N.E. Hurt and published by Springer. This book was released on 1982-12-31 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Dorothea Bahns
Publisher : Birkhäuser
ISBN 13 : 3319224077
Total Pages : 314 pages
Book Rating : 4.3/5 (192 download)
Download or read book Quantization, PDEs, and Geometry written by Dorothea Bahns and published by Birkhäuser. This book was released on 2016-02-11 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Alain Connes
Publisher : American Mathematical Soc.
ISBN 13 : 1470450453
Total Pages : 785 pages
Book Rating : 4.4/5 (74 download)
Download or read book Noncommutative Geometry, Quantum Fields and Motives written by Alain Connes and published by American Mathematical Soc.. This book was released on 2019-03-13 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.
