# lie groups and lie algebras a physicists perspective

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## Lie Groups And Lie Algebras A Physicist S Perspective

**Author :**Adam M. Bincer

**ISBN :**9780191640087

**Genre :**Science

**File Size :**63. 8 MB

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This book is intended for graduate students in Physics. It starts with a discussion of angular momentum and rotations in terms of the orthogonal group in three dimensions and the unitary group in two dimensions and goes on to deal with these groups in any dimensions. All representations of su(2) are obtained and the Wigner-Eckart theorem is discussed. Casimir operators for the orthogonal and unitary groups are discussed. The exceptional group G2 is introduced as the group of automorphisms of octonions. The symmetric group is used to deal with representations of the unitary groups and the reduction of their Kronecker products. Following the presentation of Cartan's classification of semisimple algebras Dynkin diagrams are described. The book concludes with space-time groups - the Lorentz, Poincare and Liouville groups - and a derivation of the energy levels of the non-relativistic hydrogen atom in n space dimensions.

## Lie Groups And Lie Algebras For Physicists

**Author :**Ashok Das

**ISBN :**9789814603294

**Genre :**Science

**File Size :**25. 83 MB

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The book is intended for graduate students of theoretical physics (with a background in quantum mechanics) as well as researchers interested in applications of Lie group theory and Lie algebras in physics. The emphasis is on the inter-relations of representation theories of Lie groups and the corresponding Lie algebras. Contents:Introduction to GroupsRepresentation of GroupsLie AlgebrasRelationship between Lie Algebras and Lie GroupsIrreducible Tensor Representations and Young TableauClifford AlgebraLorentz Group and the Dirac EquationYang–Mills Gauge TheoryQuark Model and SUF(3) SymmetryCasimir Invariants and Adjoint OperatorsRoot System of Lie Algebras Readership: Graduate students, researchers and anyone else with a background in quantum mechanics. Key Features:Many worked examples are included to explain the essential abstract ideas, with derivations of various results given in detailMany new features can be also found including a simple introduction to Cartan–Dynkin theory higher order Casimir invariants as well as exceptional groupsKeywords:Lie Groups;Lie Algebras;YangâMills Gauge Theory;Lorentz Group;Clifford Algebra;Dirac Equation

## Mathematical Perspectives On Theoretical Physics

**Author :**Nirmala Prakash

**ISBN :**1860943659

**Genre :**Science

**File Size :**42. 79 MB

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Readership: Upper level undergraduates, graduate students, lecturers and researchers in theoretical, mathematical and quantum physics.

## Lie Groups Physics And Geometry

**Author :**Robert Gilmore

**ISBN :**9781139469074

**Genre :**Science

**File Size :**48. 71 MB

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Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.

## Group Theory

**Author :**Predrag Cvitanović

**ISBN :**9781400837670

**Genre :**Mathematics

**File Size :**47. 12 MB

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If classical Lie groups preserve bilinear vector norms, what Lie groups preserve trilinear, quadrilinear, and higher order invariants? Answering this question from a fresh and original perspective, Predrag Cvitanovic takes the reader on the amazing, four-thousand-diagram journey through the theory of Lie groups. This book is the first to systematically develop, explain, and apply diagrammatic projection operators to construct all semi-simple Lie algebras, both classical and exceptional. The invariant tensors are presented in a somewhat unconventional, but in recent years widely used, "birdtracks" notation inspired by the Feynman diagrams of quantum field theory. Notably, invariant tensor diagrams replace algebraic reasoning in carrying out all group-theoretic computations. The diagrammatic approach is particularly effective in evaluating complicated coefficients and group weights, and revealing symmetries hidden by conventional algebraic or index notations. The book covers most topics needed in applications from this new perspective: permutations, Young projection operators, spinorial representations, Casimir operators, and Dynkin indices. Beyond this well-traveled territory, more exotic vistas open up, such as "negative dimensional" relations between various groups and their representations. The most intriguing result of classifying primitive invariants is the emergence of all exceptional Lie groups in a single family, and the attendant pattern of exceptional and classical Lie groups, the so-called Magic Triangle. Written in a lively and personable style, the book is aimed at researchers and graduate students in theoretical physics and mathematics.

## Lie Groups Lie Algebras Cohomology And Some Applications In Physics

**Author :**Josi A. de Azcárraga

**ISBN :**0521597005

**Genre :**Mathematics

**File Size :**89. 13 MB

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Now in paperback, this book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics. No previous knowledge of the mathematical theory is assumed beyond some notions of Cartan calculus and differential geometry (which are nevertheless reviewed in the book in detail). The examples, of current interest, are intended to clarify certain mathematical aspects and to show their usefulness in physical problems. The topics treated include the differential geometry of Lie groups, fibre bundles and connections, characteristic classes, index theorems, monopoles, instantons, extensions of Lie groups and algebras, some applications in supersymmetry, Chevalley-Eilenberg approach to Lie algebra cohomology, symplectic cohomology, jet-bundle approach to variational principles in mechanics, Wess-Zumino-Witten terms, infinite Lie algebras, the cohomological descent in mechanics and in gauge theories and anomalies. This book will be of interest to graduate students and researchers in theoretical physics and applied mathematics.

## Lie Algebras In Particle Physics

**Author :**Howard Georgi

**ISBN :**0813346118

**Genre :**Mathematics

**File Size :**80. 28 MB

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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.