Download or read book Differential Geometry Group Representations and Quantization written by Jörg Dieter Hennig and published by Springer. This book was released on 1991 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential geometry and analytic group theory are among the most powerful tools in mathematical physics. This volume presents review articles on a wide variety of applications of these techniques in classical continuum physics, gauge theories, quantization procedures, and the foundations of quantum theory. The articles, written by leading scientists, address both researchers and grad- uate students in mathematics, physics, and philosophy of science.
Download or read book Differential Geometry Group Representations and Quantization written by Jörg-Dieter Hennig and published by . This book was released on 2014-01-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Poisson Geometry Deformation Quantisation and Group Representations written by Simone Gutt and published by Cambridge University Press. This book was released on 2005-06-21 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to Poisson geometry suitable for graduate students.
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 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 247 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.
Download or read book Lie Groups Geometry and Representation Theory written by Victor G. Kac and published by Springer. This book was released on 2018-12-12 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 – February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant’s fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. This volume features the only published articles of important recent results of the contributors with full details of their proofs. Key topics include: Poisson structures and potentials (A. Alekseev, A. Berenstein, B. Hoffman) Vertex algebras (T. Arakawa, K. Kawasetsu) Modular irreducible representations of semisimple Lie algebras (R. Bezrukavnikov, I. Losev) Asymptotic Hecke algebras (A. Braverman, D. Kazhdan) Tensor categories and quantum groups (A. Davydov, P. Etingof, D. Nikshych) Nil-Hecke algebras and Whittaker D-modules (V. Ginzburg) Toeplitz operators (V. Guillemin, A. Uribe, Z. Wang) Kashiwara crystals (A. Joseph) Characters of highest weight modules (V. Kac, M. Wakimoto) Alcove polytopes (T. Lam, A. Postnikov) Representation theory of quantized Gieseker varieties (I. Losev) Generalized Bruhat cells and integrable systems (J.-H. Liu, Y. Mi) Almost characters (G. Lusztig) Verlinde formulas (E. Meinrenken) Dirac operator and equivariant index (P.-É. Paradan, M. Vergne) Modality of representations and geometry of θ-groups (V. L. Popov) Distributions on homogeneous spaces (N. Ressayre) Reduction of orthogonal representations (J.-P. Serre)
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 295 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.
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 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a state-of-the-art discussion of 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.
Download or read book Differential Geometry of Singular Spaces and Reduction of Symmetry written by J. Śniatycki and published by Cambridge University Press. This book was released on 2013-06-13 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author illustrates the power of the theory of subcartesian differential spaces for investigating spaces with singularities. Part I gives a detailed and comprehensive presentation of the theory of differential spaces, including integration of distributions on subcartesian spaces and the structure of stratified spaces. Part II presents an effective approach to the reduction of symmetries. Concrete applications covered in the text include reduction of symmetries of Hamiltonian systems, non-holonomically constrained systems, Dirac structures, and the commutation of quantization with reduction for a proper action of the symmetry group. With each application the author provides an introduction to the field in which relevant problems occur. This book will appeal to researchers and graduate students in mathematics and engineering.
Download or read book Classical And Quantum Systems Foundations And Symmetries Proceedings Of The 2nd International Wigner Symposium written by Heinz-dietrich Doebner and published by World Scientific. This book was released on 1993-01-19 with total page 818 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wigner Symposium series is focussed on fundamental problems and new developments in physics and their experimental, theoretical and mathematical aspects. Particular emphasis is given to those topics which have developed from the work of Eugene P Wigner. The 2nd Wigner symposium is centered around notions of symmetry and geometry, the foundations of quantum mechanics, quantum optics and particle physics. Other fields like dynamical systems, neural networks and physics of information are also represented.This volume brings together 19 plenary lectures which survey latest developments and more than 130 contributed research reports.
Download or read book Geometric And Algebraic Topological Methods In Quantum Mechanics written by Luigi Mangiarotti and published by World Scientific. This book was released on 2005-01-27 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry's geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.
Download or read book Differential Geometry of Singular Spaces and Reduction of Symmetry written by Jędrzej Śniatycki and published by Cambridge University Press. This book was released on 2013-06-13 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete presentation of the theory of differential spaces, with applications to the study of singularities in systems with symmetry.
Download or read book Methods of Noncommutative Geometry for Group C Algebras written by Do Ngoc Diep and published by CRC Press. This book was released on 1999-12-06 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description of the structure of group C*-algebras is a difficult problem, but relevant to important new developments in mathematics, such as non-commutative geometry and quantum groups. Although a significant number of new methods and results have been obtained, until now they have not been available in book form. This volume provides an introduction to and presents research on the study of group C*-algebras, suitable for all levels of readers - from graduate students to professional researchers. The introduction provides the essential features of the methods used. In Part I, the author offers an elementary overview - using concrete examples-of using K-homology, BFD functors, and KK-functors to describe group C*-algebras. In Part II, he uses advanced ideas and methods from representation theory, differential geometry, and KK-theory, to explain two primary tools used to study group C*-algebras: multidimensional quantization and construction of the index of group C*-algebras through orbit methods. The structure of group C*-algebras is an important issue both from a theoretical viewpoint and in its applications in physics and mathematics. Armed with the background, tools, and research provided in Methods of Noncommutative Geometry for Group C*-Algebras, readers can continue this work and make significant contributions to perfecting the theory and solving this problem.
Download or read book The Metaplectic Representation Mp c Structures and Geometric Quantization written by Paul Lee Robinson and published by American Mathematical Soc.. This book was released on 1989 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an account of the metaplectic representation in terms of the Bargmann-Segal model rather than the standard Schrödinger model; this allows us to describe explicitly the structure and pairing of vacuum states for positive polarizations. We develop a scheme for geometric spinors and, following Hess, using Mp[superscript italic]c structures in place of metaplectic structures.
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 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.
Download or read book Perspectives on Quantization written by Lewis A. Coburn and published by American Mathematical Soc.. This book was released on 1998 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of a 1996 Joint Summer Research Conference sponsored by AMS-IMS-SIAM on "Quantization" held at Mount Holyoke College (Northampton, MA). The purpose of this conference was to bring together researchers focusing on various mathematical aspects of quantization. In the early work of Weyl and von Neumann at the beginning of the quantum era, the setting for this enterprise was operators on Hilbert space. This setting has been expanded, especially over the past decade, to involve C*-algebras - noncommutative differential geometry and noncommutative harmonic analysis - as well as more general algebras and infinite-dimensional manifolds. The applications now include quantum field theory, notable conformal and topological field theories related to quantization of moduli spaces, and constructive quantum field theory of supersymmetric models and condensed matter physics (the fractional quantum Hall effect in particular). The spectrum of research interests which significantly intersects the topic of quantization is unusually broad including, for example, pseudodifferential analysis, the representation theory of Lie groups and algebras (including infinite-dimensional ones), operator algebras and algebraic deformation theory. The papers in this collection originated with talks by the authors at the conference and represent a strong cross-section of the interests described above.
