Deformation Quantification Theorie De Lie

Download Deformation Quantification Theorie De Lie full books in PDF, epub, and Kindle. Read online Deformation Quantification Theorie De Lie ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Déformation, quantification, théorie de Lie

Author : Alberto S. Cattaneo
Publisher : Societe Mathematique de France
ISBN 13 :
Total Pages : 210 pages
Book Rating : 4.3/5 (91 download)

DOWNLOAD NOW!

Book Synopsis Déformation, quantification, théorie de Lie by : Alberto S. Cattaneo

Download or read book Déformation, quantification, théorie de Lie written by Alberto S. Cattaneo and published by Societe Mathematique de France. This book was released on 2005 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1997, M. Kontsevich proved that every Poisson manifold admits a formal quantization, canonical up to equivalence. In doing so he solved a longstanding problem in mathematical physics. Through his proof and his interpretation of a later proof given by Tamarkin, he also opened up new research avenues in Lie theory, quantum group theory, deformation theory and the study of operads ... and uncovered fascinating links of these topics with number theory, knot theory and the theory of motives. Without doubt, his work on deformation quantization will continue to influence these fields for many years to come. In the three parts of this volume, we will 1) present the main results of Kontsevich's 1997 preprint and sketch his interpretation of Tamarkin's approach, 2) show the relevance of Kontsevich's theorem for Lie theory and 3) explain the idea from topological string theory which inspired Kontsevich's proof. An appendix is devoted to the geometry of configuration spaces.

Towards the Mathematics of Quantum Field Theory

Author : Frédéric Paugam
Publisher : Springer Science & Business Media
ISBN 13 : 3319045644
Total Pages : 485 pages
Book Rating : 4.3/5 (19 download)

DOWNLOAD NOW!

Book Synopsis Towards the Mathematics of Quantum Field Theory by : Frédéric Paugam

Download or read book Towards the Mathematics of Quantum Field Theory written by Frédéric Paugam and published by Springer Science & Business Media. This book was released on 2014-02-20 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ambitious and original book sets out to introduce to mathematicians (even including graduate students ) the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in use. This in turn promotes the interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, though mathematicians are the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature. The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second part presents a large family of examples of classical field theories, both from experimental and theoretical physics, while the third part provides an introduction to quantum field theory, presents various renormalization methods, and discusses the quantization of factorization algebras.

Kontsevich’s Deformation Quantization and Quantum Field Theory

Author : Nima Moshayedi
Publisher : Springer Nature
ISBN 13 : 303105122X
Total Pages : 345 pages
Book Rating : 4.0/5 (31 download)

DOWNLOAD NOW!

Book Synopsis Kontsevich’s Deformation Quantization and Quantum Field Theory by : Nima Moshayedi

Download or read book Kontsevich’s Deformation Quantization and Quantum Field Theory written by Nima Moshayedi and published by Springer Nature. This book was released on 2022-08-11 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to deformation quantization and its relation to quantum field theory, with a focus on the constructions of Kontsevich and Cattaneo & Felder. This subject originated from an attempt to understand the mathematical structure when passing from a commutative classical algebra of observables to a non-commutative quantum algebra of observables. Developing deformation quantization as a semi-classical limit of the expectation value for a certain observable with respect to a special sigma model, the book carefully describes the relationship between the involved algebraic and field-theoretic methods. The connection to quantum field theory leads to the study of important new field theories and to insights in other parts of mathematics such as symplectic and Poisson geometry, and integrable systems. Based on lectures given by the author at the University of Zurich, the book will be of interest to graduate students in mathematics or theoretical physics. Readers will be able to begin the first chapter after a basic course in Analysis, Linear Algebra and Topology, and references are provided for more advanced prerequisites.

Hochschild Cohomology for Algebras

Author : Sarah J. Witherspoon
Publisher : American Mathematical Soc.
ISBN 13 : 1470449315
Total Pages : 264 pages
Book Rating : 4.4/5 (74 download)

DOWNLOAD NOW!

Book Synopsis Hochschild Cohomology for Algebras by : Sarah J. Witherspoon

Download or read book Hochschild Cohomology for Algebras written by Sarah J. Witherspoon and published by American Mathematical Soc.. This book was released on 2019-12-10 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a thorough and self-contained introduction to the theory of Hochschild cohomology for algebras and includes many examples and exercises. The book then explores Hochschild cohomology as a Gerstenhaber algebra in detail, the notions of smoothness and duality, algebraic deformation theory, infinity structures, support varieties, and connections to Hopf algebra cohomology. Useful homological algebra background is provided in an appendix. The book is designed both as an introduction for advanced graduate students and as a resource for mathematicians who use Hochschild cohomology in their work.

Lie Methods in Deformation Theory

Author : Marco Manetti
Publisher : Springer Nature
ISBN 13 : 9811911851
Total Pages : 576 pages
Book Rating : 4.8/5 (119 download)

DOWNLOAD NOW!

Book Synopsis Lie Methods in Deformation Theory by : Marco Manetti

Download or read book Lie Methods in Deformation Theory written by Marco Manetti and published by Springer Nature. This book was released on 2022-08-01 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book furnishes a comprehensive treatment of differential graded Lie algebras, L-infinity algebras, and their use in deformation theory. We believe it is the first textbook devoted to this subject, although the first chapters are also covered in other sources with a different perspective. Deformation theory is an important subject in algebra and algebraic geometry, with an origin that dates back to Kodaira, Spencer, Kuranishi, Gerstenhaber, and Grothendieck. In the last 30 years, a new approach, based on ideas from rational homotopy theory, has made it possible not only to solve long-standing open problems, but also to clarify the general theory and to relate apparently different features. This approach works over a field of characteristic 0, and the central role is played by the notions of differential graded Lie algebra, L-infinity algebra, and Maurer–Cartan equations. The book is written keeping in mind graduate students with a basic knowledge of homological algebra and complex algebraic geometry as utilized, for instance, in the book by K. Kodaira, Complex Manifolds and Deformation of Complex Structures. Although the main applications in this book concern deformation theory of complex manifolds, vector bundles, and holomorphic maps, the underlying algebraic theory also applies to a wider class of deformation problems, and it is a prerequisite for anyone interested in derived deformation theory. Researchers in algebra, algebraic geometry, algebraic topology, deformation theory, and noncommutative geometry are the major targets for the book.

Higher Structures in Geometry and Physics

Author : Alberto S. Cattaneo
Publisher : Springer Science & Business Media
ISBN 13 : 081764735X
Total Pages : 371 pages
Book Rating : 4.8/5 (176 download)

DOWNLOAD NOW!

Book Synopsis Higher Structures in Geometry and Physics by : Alberto S. Cattaneo

Download or read book Higher Structures in Geometry and Physics written by Alberto S. Cattaneo and published by Springer Science & Business Media. This book was released on 2010-11-25 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics— such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics— and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. The volume is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures.

Quantization, Geometry and Noncommutative Structures in Mathematics and Physics

Author : Alexander Cardona
Publisher : Springer
ISBN 13 : 3319654276
Total Pages : 347 pages
Book Rating : 4.3/5 (196 download)

DOWNLOAD NOW!

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 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.

Deformation Quantization

Author : Gilles Halbout
Publisher : Walter de Gruyter
ISBN 13 : 3110866226
Total Pages : 244 pages
Book Rating : 4.1/5 (18 download)

DOWNLOAD NOW!

Book Synopsis Deformation Quantization by : Gilles Halbout

Download or read book Deformation Quantization written by Gilles Halbout and published by Walter de Gruyter. This book was released on 2012-10-25 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains eleven refereed research papers on deformation quantization by leading experts in the respective fields. These contributions are based on talks presented on the occasion of the meeting between mathematicians and theoretical physicists held in Strasbourg in May 2001. Topics covered are: star-products over Poisson manifolds, quantization of Hopf algebras, index theorems, globalization and cohomological problems. Both the mathematical and the physical approach ranging from asymptotic quantum electrodynamics to operads and prop theory will be presented. Historical remarks and surveys set the results presented in perspective. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume will give an overview of a field of research that has seen enourmous acticity in the last years, with new ties to many other areas of mathematics and physics.

Groupoids in Analysis, Geometry, and Physics

Author : Arlan Ramsay
Publisher : American Mathematical Soc.
ISBN 13 : 0821820427
Total Pages : 208 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Groupoids in Analysis, Geometry, and Physics by : Arlan Ramsay

Download or read book Groupoids in Analysis, Geometry, and Physics written by Arlan Ramsay and published by American Mathematical Soc.. This book was released on 2001 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groupoids often occur when there is symmetry of a nature not expressible in terms of groups. Other uses of groupoids can involve something of a dynamical nature. Indeed, some of the main examples come from group actions. It should also be noted that in many situations where groupoids have been used, the main emphasis has not been on symmetry or dynamics issues. While the implicit symmetry and dynamics are relevant, the groupoid records mostly the structure of the space of leaves and the holonomy. More generally, the use of groupoids is very much related to various notions of orbit equivalance. This book presents the proceedings from the Joint Summer Research Conference on ``Groupoids in Analysis, Geometry, and Physics'' held in Boulder, CO. The book begins with an introduction to ways in which groupoids allow a more comprehensive view of symmetry than is seen via groups. Topics range from foliations, pseudo-differential operators, $KK$-theory, amenability, Fell bundles, and index theory to quantization of Poisson manifolds. Readers will find examples of important tools for working with groupoids. This book is geared to students and researchers. It is intended to improve their understanding of groupoids and to encourage them to look further while learning about the tools used.

Algebraic Operads

Author : Jean-Louis Loday
Publisher : Springer Science & Business Media
ISBN 13 : 3642303625
Total Pages : 649 pages
Book Rating : 4.6/5 (423 download)

DOWNLOAD NOW!

Book Synopsis Algebraic Operads by : Jean-Louis Loday

Download or read book Algebraic Operads written by Jean-Louis Loday and published by Springer Science & Business Media. This book was released on 2012-08-08 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many areas of mathematics some “higher operations” are arising. These havebecome so important that several research projects refer to such expressions. Higher operationsform new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the Homotopy Transfer Theorem. Although the necessary notions of algebra are recalled, readers are expected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included. After a low-level chapter on Algebra, accessible to (advanced) undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices review the basic results needed in order to understand the various chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers.

Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry

Author : Damien Calaque
Publisher : European Mathematical Society
ISBN 13 : 9783037190968
Total Pages : 120 pages
Book Rating : 4.1/5 (99 download)

DOWNLOAD NOW!

Book Synopsis Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry by : Damien Calaque

Download or read book Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry written by Damien Calaque and published by European Mathematical Society. This book was released on 2011 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Duflo isomorphism first appeared in Lie theory and representation theory. It is an isomorphism between invariant polynomials of a Lie algebra and the center of its universal enveloping algebra, generalizing the pioneering work of Harish-Chandra on semi-simple Lie algebras. Kontsevich later refined Duflo's result in the framework of deformation quantization and also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. This book, which arose from a series of lectures by Damien Calaque at ETH, derives these two isomorphisms from a Duflo-type result for $Q$-manifolds. All notions mentioned above are introduced and explained in this book. The only prerequisites are basic linear algebra and differential geometry. In addition to standard notions such as Lie (super) algebras, complex manifolds, Hochschild and Chevalley-Eilenberg cohomologies, spectral sequences, Atiyah and Todd classes, the graphical calculus introduced by Kontsevich in his seminal work on deformation quantization is addressed in detail. This book is well suited for graduate students in mathematics and mathematical physics as well as researchers working in Lie theory, algebraic geometry, and deformation theory.

Poisson Structures

Author : Camille Laurent-Gengoux
Publisher : Springer Science & Business Media
ISBN 13 : 3642310907
Total Pages : 470 pages
Book Rating : 4.6/5 (423 download)

DOWNLOAD NOW!

Book Synopsis Poisson Structures by : Camille Laurent-Gengoux

Download or read book Poisson Structures written by Camille Laurent-Gengoux and published by Springer Science & Business Media. This book was released on 2012-08-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.

CRC Handbook of Lie Group Analysis of Differential Equations

Author : Nail H. Ibragimov
Publisher : CRC Press
ISBN 13 : 9780849344886
Total Pages : 452 pages
Book Rating : 4.3/5 (448 download)

DOWNLOAD NOW!

Book Synopsis CRC Handbook of Lie Group Analysis of Differential Equations by : Nail H. Ibragimov

Download or read book CRC Handbook of Lie Group Analysis of Differential Equations written by Nail H. Ibragimov and published by CRC Press. This book was released on 1993-10-20 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra. Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Bäcklund, conditional and non-classical symmetries, approximate symmetry groups for equations with a small parameter, group analysis of differential equations with distributions, integro-differential equations, recursions, and symbolic software packages. The text provides an ideal introduction to the modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.

CRC Handbook of Lie Group Analysis of Differential Equations, Volume I

Author : Nail H. Ibragimov
Publisher : CRC Press
ISBN 13 : 1000941426
Total Pages : 444 pages
Book Rating : 4.0/5 (9 download)

DOWNLOAD NOW!

Book Synopsis CRC Handbook of Lie Group Analysis of Differential Equations, Volume I by : Nail H. Ibragimov

Download or read book CRC Handbook of Lie Group Analysis of Differential Equations, Volume I written by Nail H. Ibragimov and published by CRC Press. This book was released on 2023-08-25 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra. Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Bäcklund, conditional and non-classical symmetries, approximate symmetry groups for equations with a small parameter, group analysis of differential equations with distributions, integro-differential equations, recursions, and symbolic software packages. The text provides an ideal introduction to the modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.

Formality Theory

Author : Chiara Esposito
Publisher : Springer
ISBN 13 : 3319092901
Total Pages : 98 pages
Book Rating : 4.3/5 (19 download)

DOWNLOAD NOW!

Book Synopsis Formality Theory by : Chiara Esposito

Download or read book Formality Theory written by Chiara Esposito and published by Springer. This book was released on 2014-09-04 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 932 pages
Book Rating : 4.3/5 (91 download)

DOWNLOAD NOW!

Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Abstract And Applied Analysis - Proceedings Of The International Conference

Author : Nguyen Minh Chuong
Publisher : World Scientific
ISBN 13 : 9814482110
Total Pages : 579 pages
Book Rating : 4.8/5 (144 download)

DOWNLOAD NOW!

Book Synopsis Abstract And Applied Analysis - Proceedings Of The International Conference by : Nguyen Minh Chuong

Download or read book Abstract And Applied Analysis - Proceedings Of The International Conference written by Nguyen Minh Chuong and published by World Scientific. This book was released on 2004-06-01 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods.Topics include linear elliptic systems for composite material — the coefficients may jump from domain to domain; Stochastic Analysis — many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences