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Quantization Pdes And Geometry
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Book Synopsis Quantization, PDEs, and Geometry by : Dorothea Bahns
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.
Book Synopsis Geometry of PDEs and Mechanics by : Agostino Prastaro
Download or read book Geometry of PDEs and Mechanics written by Agostino Prastaro and published by World Scientific. This book was released on 1996 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the theory of partial differential equations (PDEs) from a modern geometric point of view so that PDEs can be characterized by using either technique of differential geometry or algebraic geometry. This allows us to recognize the richness of the structure of PDEs. It presents, for the first time, a geometric theory of non-commutative (quantum) PDEs and gives a general application of this theory to quantum field theory and quantum supergravity.
Book Synopsis Geometry and Quantization of Moduli Spaces by : Vladimir Fock
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.
Book Synopsis Differential Geometry, Group Representations, and Quantization by : Jörg Dieter Hennig
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.
Book Synopsis Quantized Partial Differential Equations by : Agostino Prastaro
Download or read book Quantized Partial Differential Equations written by Agostino Prastaro and published by World Scientific. This book was released on 2004 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents, for the first time, a systematic formulation ofthe geometric theory of noncommutative PDE''s which is suitable enoughto be used for a mathematical description of quantum dynamics andquantum field theory. A geometric theory of supersymmetric quantumPDE''s is also considered, in order to describe quantumsupergravity. Covariant and canonical quantizations of (super) PDE''sare shown to be founded on the geometric theory of PDE''s and toproduce quantum (super) PDE''s by means of functors from the categoryof commutative (super) PDE''s to the category of quantum (super)PDE''s. Global properties of solutions to (super) (commutative) PDE''sare obtained by means of their integral bordism groups.
Book Synopsis Non-linear Partial Differential Operators and Quantization Procedures by : S.I. Andersson
Download or read book Non-linear Partial Differential Operators and Quantization Procedures written by S.I. Andersson and published by Springer. This book was released on 2006-11-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantization, Geometry and Noncommutative Structures in Mathematics and Physics by : Alexander Cardona
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.
Book Synopsis Lectures on the Geometry of Quantization by : Sean Bates
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.
Book Synopsis Coherent Transform, Quantization and Poisson Geometry by : Mikhail Vladimirovich Karasev
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.
Book Synopsis Differential Geometry, Group Representations, and Quantization by : Jörg-Dieter Hennig
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:
Book Synopsis The Interplay between Differential Geometry and Differential Equations by : Valentin Vasilʹevich Lychagin
Download or read book The Interplay between Differential Geometry and Differential Equations written by Valentin Vasilʹevich Lychagin and published by American Mathematical Soc.. This book was released on 1995 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Arithmetic and Geometry Around Quantization by : Özgür Ceyhan
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.
Book Synopsis Non-linear Partial Differential Operators and Quantization Procedures by : S. I. Andersson
Download or read book Non-linear Partial Differential Operators and Quantization Procedures written by S. I. Andersson and published by . This book was released on 1983 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Poisson Brackets by : Mikhail Vladimirovich Karasev
Download or read book Nonlinear Poisson Brackets written by Mikhail Vladimirovich Karasev and published by American Mathematical Soc.. This book was released on 1993 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to describe in detail the new objects that appear in the solution of these problems. Many ideas of algebra, modern differential geometry, algebraic topology, and operator theory are synthesized here. The authors prove all statements in detail, thus making the book accessible to graduate students.
Book Synopsis Operators, Geometry and Quanta by : Dmitri Fursaev
Download or read book Operators, Geometry and Quanta written by Dmitri Fursaev and published by Springer Science & Business Media. This book was released on 2011-06-25 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.
Book Synopsis Nonlinear Poisson Brackets by : Mihail Vladimirovi_ Karasev
Download or read book Nonlinear Poisson Brackets written by Mihail Vladimirovi_ Karasev and published by American Mathematical Soc.. This book was released on 2012-06-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to describe in detail the new objects that appear in the solution of these problems. Many ideas of algebra, modern differential geometry, algebraic topology, and operator theory are synthesized here. The authors prove all statements in detail, thus making the book accessible to graduate students.
Book Synopsis Loop Spaces, Characteristic Classes and Geometric Quantization by : Jean-Luc Brylinski
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 2009-12-30 with total page 318 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.
