Lie Algebras And Applications

Author : Francesco Iachello
Publisher : Springer
ISBN 13 : 3540362398
Total Pages : 196 pages
Book Rating : 4.95/5 ( download)

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Download or read book Lie Algebras and Applications written by Francesco Iachello and published by Springer. This book was released on 2007-02-22 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, designed for advanced graduate students and post-graduate researchers, introduces Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. The book contains many examples that help to elucidate the abstract algebraic definitions. It provides a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators and the dimensions of the representations of all classical Lie algebras.

Author : Robert Gilmore
Publisher : Courier Corporation
ISBN 13 : 0486131564
Total Pages : 610 pages
Book Rating : 4.66/5 ( download)

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Download or read book Lie Groups, Lie Algebras, and Some of Their Applications written by Robert Gilmore and published by Courier Corporation. This book was released on 2012-05-23 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.

Author : Peter J. Olver
Publisher : Springer Science & Business Media
ISBN 13 : 1468402749
Total Pages : 524 pages
Book Rating : 4.42/5 ( download)

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Download or read book Applications of Lie Groups to Differential Equations written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.

Author : D.H. Sattinger
Publisher : Springer Science & Business Media
ISBN 13 : 1475719108
Total Pages : 218 pages
Book Rating : 4.09/5 ( download)

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Download or read book Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics written by D.H. Sattinger and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselves to the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.

Author : Willi-Hans Steeb
Publisher : World Scientific Publishing Company
ISBN 13 : 9813104112
Total Pages : 352 pages
Book Rating : 4.12/5 ( download)

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Download or read book Problems and Solutions for Groups, Lie Groups, Lie Algebras with Applications written by Willi-Hans Steeb and published by World Scientific Publishing Company. This book was released on 2012-04-26 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents examples of important techniques and theorems for Groups, Lie groups and Lie algebras. This allows the reader to gain understandings and insights through practice. Applications of these topics in physics and engineering are also provided. The book is self-contained. Each chapter gives an introduction to the topic.

Author : M. Goze
Publisher : Springer Science & Business Media
ISBN 13 : 9401724326
Total Pages : 350 pages
Book Rating : 4.26/5 ( download)

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Download or read book Nilpotent Lie Algebras written by M. Goze and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the theory of nilpotent Lie algebras and their applications. Nilpotent Lie algebras have played an important role over the last years both in the domain of algebra, considering its role in the classification problems of Lie algebras, and in the domain of differential geometry. Among the topics discussed here are the following: cohomology theory of Lie algebras, deformations and contractions, the algebraic variety of the laws of Lie algebras, the variety of nilpotent laws, and characteristically nilpotent Lie algebras in nilmanifolds. Audience: This book is intended for graduate students specialising in algebra, differential geometry and in theoretical physics and for researchers in mathematics and in theoretical physics.

Author : Robert N. Cahn
Publisher : Courier Corporation
ISBN 13 : 0486150313
Total Pages : 180 pages
Book Rating : 4.14/5 ( download)

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Download or read book Semi-Simple Lie Algebras and Their Representations written by Robert N. Cahn and published by Courier Corporation. This book was released on 2014-06-10 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed to acquaint students of particle physiME already familiar with SU(2) and SU(3) with techniques applicable to all simple Lie algebras, this text is especially suited to the study of grand unification theories. Author Robert N. Cahn, who is affiliated with the Lawrence Berkeley National Laboratory in Berkeley, California, has provided a new preface for this edition. Subjects include the killing form, the structure of simple Lie algebras and their representations, simple roots and the Cartan matrix, the classical Lie algebras, and the exceptional Lie algebras. Additional topiME include Casimir operators and Freudenthal's formula, the Weyl group, Weyl's dimension formula, reducing product representations, subalgebras, and branching rules. 1984 edition.

Author : Josi A. de Azcárraga
Publisher : Cambridge University Press
ISBN 13 : 9780521597005
Total Pages : 480 pages
Book Rating : 4.05/5 ( download)

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Download or read book Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics written by Josi A. de Azcárraga and published by Cambridge University Press. This book was released on 1998-08-06 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.

Author : Johan G. F. Belinfante
Publisher : SIAM
ISBN 13 : 9781611971330
Total Pages : 175 pages
Book Rating : 4.30/5 ( download)

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Download or read book A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods written by Johan G. F. Belinfante and published by SIAM. This book was released on 1989-01-01 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the concepts and methods of the Lie theory in a form accessible to the non-specialist by keeping mathematical prerequisites to a minimum. Although the authors have concentrated on presenting results while omitting most of the proofs, they have compensated for these omissions by including many references to the original literature. Their treatment is directed toward the reader seeking a broad view of the subject rather than elaborate information about technical details. Illustrations of various points of the Lie theory itself are found throughout the book in material on applications. In this reprint edition, the authors have resisted the temptation of including additional topics. Except for correcting a few minor misprints, the character of the book, especially its focus on classical representation theory and its computational aspects, has not been changed.

Author : K. Erdmann
Publisher : Springer Science & Business Media
ISBN 13 : 1846284902
Total Pages : 251 pages
Book Rating : 4.08/5 ( download)

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Download or read book Introduction to Lie Algebras written by K. Erdmann and published by Springer Science & Business Media. This book was released on 2006-09-28 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.