**ISBN:** 0805316000

**Author:** Robert N. Cahn

**Language:** English

**Publisher:** Benjamin / Cummings Publishing Company (June 1, 1984)

**Pages:** 153

**Category:** Mathematics

**Subcategory:** Science

**Rating:** 4.5

**Votes:** 737

**Size Fb2:** 1382 kb

**Size ePub:** 1391 kb

**Size Djvu:** 1352 kb

**Other formats:** doc txt mbr rtf

Bibliographic information. Title Robert N. Cahn. Benjamin-Cummings Publishing Company, 1984.

Bibliographic information. Semi-Simple Lie Algebras and Their Representations Volume 59 of Frontiers in physics Volume 59 of Frontiers in Physics : a lecture note and reprint series.

all of the properties of the simple Lie algebra to which it corresponds The objective of this book is to provide a readable synthesis of the theory of (complex) semisimple Lie algebras and their representations which are usually needed in physics.

all of the properties of the simple Lie algebra to which it corresponds. The author shows how the contents of the Cartan matrix can be summarized in terms of 'Dynkin diagrams'. These considerations allow an explicit characterization of the 'classical' Lie algebras: SU(n), SO(n), and Sp(2n) in chapter 8. The Dynkin diagrams of these Lie algebras are constructed. Then in chapter 9, the author considers the 'exceptional' Lie algebras, which are the last of the simple Lie algebras (5 in all). The objective of this book is to provide a readable synthesis of the theory of (complex) semisimple Lie algebras and their representations which are usually needed in physics.

Designed to acquaint students of particle physics 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

Designed to acquaint students of particle physics 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. Subjects include simple roots and the Cartan matrix, the classical and exceptional Lie algebras, the Weyl group, and more.

Author Robert N. Cahn, who is affiliated with the Lawrence Berkeley National Laboratory in Berkeley, California, has .

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 topics include Casimir operators and Freudenthal's formula, the Weyl group, Weyl's dimension formula, reducing product representations, subalgebras, and branching rules. Read on the Scribd mobile app.

Semi-Simple Lie Algebras and Their Representations. The sources of this book are the classical exposition of Jacobson in his Lie Algebras and three great papers of . Lawrence Berkeley Laboratory University of California Berkeley, California. Particle physics has been revolutionized by the development of a new paradigm, that of gauge theories. The SU(2) x U(1) theory of electroweak in-teractions and the color SU(3) theory of strong interactions provide the present explanation of three of the four previously distinct forces. A listing of the references is given in the Bibliography. In addition, at the end of each chapter, references.

The sources of this book are the classical exposition of Jacobson in his Lie Algebras and three great papers of .

i Semi-Simple Lie Algebras and Their Representations Robert N. Cahn Lawrence Berkeley Laboratory University of California Berkeley, California 1984 THE BENJAMIN/CUMMINGS PUBLISHING COMPANY Advanced Book.

There is a natural connection between particle physics and representation theory, as first noted in the 1930s by Eugene Wigner. According to this connection, the different quantum states of an elementary particle give rise to an irreducible representation of the Poincaré group.

oceedings{, title {Semi-Simple Lie Algebras and Their Representations}, author {Robert .

oceedings{, title {Semi-Simple Lie Algebras and Their Representations}, author {Robert Cahn}, year {1984} }. Robert Cahn. This paper presents an overview of the representations of Lie algebras, particularly semi-simple Lie algebras, with a view towards theoretical physics.

matrix, the classical and exceptional Lie algebras, the Weyl group, and more.

You can download the book or read it online. Description: Designed to acquaint students of particle physics 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.

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