Symmetries Lie Algebras And Representations

Author: Jürgen Fuchs
Publisher: Cambridge University Press
ISBN: 0521541190
Size: 18.70 MB
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This book gives an introduction to Lie algebras and their representations. Lie algebras have many applications in mathematics and physics, and any physicist or applied mathematician must nowadays be well acquainted with them.

Lie Algebras In Particle Physics

Author: Howard Georgi
Publisher: Westview Press
ISBN: 0813346118
Size: 15.29 MB
Format: PDF, Mobi
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Howard Georgi is the co-inventor (with Sheldon Glashow) of the SU(5) theory. This extensively revised and updated edition of his classic text makes the theory of Lie groups accessible to graduate students, while offering a perspective on the way in which knowledge of such groups can provide an insight into the development of unified theories of strong, weak, and electromagnetic interactions.

Continuous Symmetries Lie Algebras Differential Equations And Computer Algebra

Author: Willi-Hans Steeb
Publisher: World Scientific Publishing Company
ISBN: 9789813107014
Size: 19.81 MB
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This textbook comprehensively introduces students and researchers to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations. Covering all the modern techniques in detail, it relates applications to cutting-edge research fields such as Yang–Mills theory and string theory. Aimed at readers in applied mathematics and physics rather than pure mathematics, the material is ideally suited to students and researchers whose main interest lies in finding solutions to differential equations and invariants of maps. A large number of worked examples and challenging exercises help readers to work independently of teachers, and by including SymbolicC++ implementations of the techniques in each chapter, the book takes full advantage of the advancements in algebraic computation. Twelve new sections have been added in this edition, including: Haar measure, Sato's theory and sigma functions, universal algebra, anti-self dual Yang-Mills equation, and discrete Painlevé equations. Errata(s) Errata

Symmetry Representations And Invariants

Author: Roe Goodman
Publisher: Springer Science & Business Media
ISBN: 9780387798523
Size: 18.43 MB
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Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete arguments now given in the general case. Key Features of Symmetry, Representations, and Invariants: (1) Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus; (2) Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux); (3) Self-contained chapters, appendices, comprehensive bibliography; (4) More than 350 exercises (most with detailed hints for solutions) further explore main concepts; (5) Serves as an excellent main text for a one-year course in Lie group theory; (6) Benefits physicists as well as mathematicians as a reference work.

Lie Groups

Author: Claudio Procesi
Publisher: Springer Science & Business Media
ISBN: 9780387289298
Size: 20.14 MB
Format: PDF
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Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. In Lie Groups: An Approach through Invariants and Representations, the author's masterful approach gives the reader a comprehensive treatment of the classical Lie groups along with an extensive introduction to a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group representations, invariants, Hilbert theory, and binary forms with fields ranging from pure algebra to functional analysis. By covering sufficient background material, the book is made accessible to a reader with a relatively modest mathematical background. Historical information, examples, exercises are all woven into the text. This unique exposition is suitable for a broad audience, including advanced undergraduates, graduates, mathematicians in a variety of areas from pure algebra to functional analysis and mathematical physics.

The Lie Algebras Su N

Author: Walter Pfeifer
Publisher: Springer Science & Business Media
ISBN: 376432418X
Size: 14.22 MB
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Lie algebras are efficient tools for analyzing the properties of physical systems. Concrete applications comprise the formulation of symmetries of Hamiltonian systems, the description of atomic, molecular and nuclear spectra, the physics of elementary particles and many others. This work gives an introduction to the properties and the structure of the Lie algebras su(n). First, characteristic quantities such as structure constants, the Killing form and functions of Lie algebras are introduced. The properties of the algebras su(2), su(3) and su(4) are investigated in detail. Geometric models of the representations are developed. A lot of care is taken over the use of the term "multiplet of an algebra". The book features an elementary (matrix) access to su(N)-algebras, and gives a first insight into Lie algebras. Student readers should be enabled to begin studies on physical su(N)-applications, instructors will profit from the detailed calculations and examples.