Theory Of Groups And Symmetries: Finite Groups, Lie Groups, And Lie Algebras

DOWNLOAD NOW »

Author: Rubakov Valery A,Isaev Alexey P

Publisher: World Scientific

ISBN: 9813236876

Category: Science

Page: 476

View: 6607

The book presents the main approaches in study of algebraic structures of symmetries in models of theoretical and mathematical physics, namely groups and Lie algebras and their deformations. It covers the commonly encountered quantum groups (including Yangians). The second main goal of the book is to present a differential geometry of coset spaces that is actively used in investigations of models of quantum field theory, gravity and statistical physics. The third goal is to explain the main ideas about the theory of conformal symmetries, which is the basis of the AdS/CFT correspondence. The theory of groups and symmetries is an important part of theoretical physics. In elementary particle physics, cosmology and related fields, the key role is played by Lie groups and algebras corresponding to continuous symmetries. For example, relativistic physics is based on the Lorentz and Poincare groups, and the modern theory of elementary particles — the Standard Model — is based on gauge (local) symmetry with the gauge group SU(3) x SU(2) x U(1). This book presents constructions and results of a general nature, along with numerous concrete examples that have direct applications in modern theoretical and mathematical physics. Contents: Preface Groups and Transformations Lie Groups Lie Algebras Representations of Groups and Lie Algebras Compact Lie Algebras Root Systems and Classification of Simple Lie Algebras Homogeneous Spaces and their Geometry Solutions to Selected Problems Selected Bibliography References Index Readership: Graduate students and researchers in theoretical physics and mathematical physics. Keywords: Lie Groups;Lie Algebras;Representation Theory;Conformal Symmetries;Yangians;Coset Spaces;Differential Geometry;Casimir Operators;Root Systems;AdS Spaces;Lobachevskian GeometryReview:0

Mathematical Tools for Physicists

DOWNLOAD NOW »

Author: Michael Grinfeld

Publisher: John Wiley & Sons

ISBN: 3527684271

Category: Science

Page: 632

View: 3360

The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Quantization on Nilpotent Lie Groups

DOWNLOAD NOW »

Author: Veronique Fischer,Michael Ruzhansky

Publisher: Birkhäuser

ISBN: 3319295586

Category: Mathematics

Page: 557

View: 7172

This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups. The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.

Function Spaces and Partial Differential Equations

2 Volume set

DOWNLOAD NOW »

Author: Ali Taheri

Publisher: OUP Oxford

ISBN: 0191047821

Category: Mathematics

Page: 500

View: 6288

This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Function Spaces and Partial Differential Equations

DOWNLOAD NOW »

Author: Ali Taheri

Publisher: Oxford University Press, USA

ISBN: 0198733151

Category: Differential equations, Partial

Page: 480

View: 2386

This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Classical Algebraic Geometry

A Modern View

DOWNLOAD NOW »

Author: Igor V. Dolgachev

Publisher: Cambridge University Press

ISBN: 1139560786

Category: Mathematics

Page: N.A

View: 9191

Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.

Field Representations and Introduction to Scattering

DOWNLOAD NOW »

Author: V. V. Varadan,Akhlesh Lakhtakia,Vijay K. Varadan

Publisher: N.A

ISBN: N.A

Category: Technology & Engineering

Page: 355

View: 8092

This is the first volume in the Handbook on Acoustic, Electromagnetic and Elastic Wave Scattering subseries and it serves as an introduction to the remaining volumes. The basic objective of this series is to serve as a major reference source for the uniform treatment of acoustic, electromagnetic and elastodynamic field problems. It provides an indispensable guide for the scientific community and graduate students by acquainting them very quickly with the basic principles of a certain technique as it is applied to any of the three fields, and also provides appropriate references. It was felt that in presenting such a comprehensive collection of treatment methods as they are applied to all three wave fields it would open up a whole range of new ideas to solid mechanists, who would perhaps otherwise not come into contact with such electromagnetic waves literature. These three subseries of volumes will prove a useful aid to researchers in reading and understanding the jargon used in the literature on acoustic, electromagnetic and elastodynamic fields, as well as providing them with the opportunity for the cross-fertilization of ideas.

Applications of nonlinear analysis in the physical sciences

invited papers presented at a workshop at Bielefeld, Federal Republic of Germany, 1-10 October 1979

DOWNLOAD NOW »

Author: Herbert Amann,N. Bazley,K. Kirchgässner

Publisher: Pitman Advanced Publishing Program

ISBN: N.A

Category: Mathematics

Page: 325

View: 7675

Report AM-R

DOWNLOAD NOW »

Author: Centrum voor Wiskunde en Informatica (Amsterdam, Netherlands) Department of Applied Mathematics,Mathematisch Centrum (Amsterdam, Netherlands)

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 6915

The Mathematical Legacy of Wilhelm Magnus

Groups, Geometry, and Special Functions : Conference on the Legacy of Wilhelm Magnus, May 1-3, 1992, Polytechnic University, Brooklyn, New York

DOWNLOAD NOW »

Author: William Abikoff,Joan S. Birman,Kathryn Kuiken

Publisher: American Mathematical Soc.

ISBN: 082185156X

Category: Mathematics

Page: 499

View: 4446

Wilhelm Magnus was an extraordinarily creative mathematician who made fundamental contributions to diverse areas, including group theory, geometry, and special functions. This book contains the proceedings of a conference held in May 1992 at Polytechnic University to honor the memory of Magnus. The focus of the book is on active areas of current research where Magnus' influence can be seen. The papers range from expository articles to major new research, bringing together seemingly diverse topics and providing entry points to a variety of areas of mathematics.