Lie Groups and Lie Algebras - A Physicist's Perspective

Lie Groups and Lie Algebras - A Physicist's Perspective
Author: Adam M. Bincer
Publisher: Oxford University Press
Total Pages: 216
Release: 2013
Genre: Mathematics
ISBN: 0199662924

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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 - A Physicist's Perspective

Lie Groups and Lie Algebras - A Physicist's Perspective
Author: Adam M. Bincer
Publisher: OUP Oxford
Total Pages: 216
Release: 2012-10-11
Genre: Science
ISBN: 0191640085

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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 Algebras with Applications to Physics, Geometry, and Mechanics

Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics
Author: D.H. Sattinger
Publisher: Springer Science & Business Media
Total Pages: 218
Release: 2013-11-11
Genre: Mathematics
ISBN: 1475719108

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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.

Lie Groups, Physics, and Geometry

Lie Groups, Physics, and Geometry
Author: Robert Gilmore
Publisher: Cambridge University Press
Total Pages: 5
Release: 2008-01-17
Genre: Science
ISBN: 113946907X

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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.

Lie Groups And Lie Algebras For Physicists

Lie Groups And Lie Algebras For Physicists
Author: Ashok Das
Publisher: World Scientific
Total Pages: 358
Release: 2014-09-03
Genre: Science
ISBN: 9814603295

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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.

Lie Algebras In Particle Physics

Lie Algebras In Particle Physics
Author: Howard Georgi
Publisher: Westview Press
Total Pages: 340
Release: 1999-10-22
Genre: Science
ISBN: 0738202339

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An exciting new edition of a classic text

Differential Geometry and Lie Groups for Physicists

Differential Geometry and Lie Groups for Physicists
Author: Marián Fecko
Publisher: Cambridge University Press
Total Pages: 11
Release: 2006-10-12
Genre: Science
ISBN: 1139458035

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Covering subjects including manifolds, tensor fields, spinors, and differential forms, this textbook introduces geometrical topics useful in modern theoretical physics and mathematics. It develops understanding through over 1000 short exercises, and is suitable for advanced undergraduate or graduate courses in physics, mathematics and engineering.

Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics

Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics
Author: Josi A. de Azcárraga
Publisher: Cambridge University Press
Total Pages: 480
Release: 1998-08-06
Genre: Mathematics
ISBN: 9780521597005

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A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.

Group Theory in a Nutshell for Physicists

Group Theory in a Nutshell for Physicists
Author: A. Zee
Publisher: Princeton University Press
Total Pages: 632
Release: 2016-03-29
Genre: Science
ISBN: 1400881188

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A concise, modern textbook on group theory written especially for physicists Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-contained textbook on the subject written especially for physicists. Group Theory in a Nutshell for Physicists fills this gap, providing a user-friendly and classroom-tested text that focuses on those aspects of group theory physicists most need to know. From the basic intuitive notion of a group, A. Zee takes readers all the way up to how theories based on gauge groups could unify three of the four fundamental forces. He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study. Provides physicists with a modern and accessible introduction to group theory Covers applications to various areas of physics, including field theory, particle physics, relativity, and much more Topics include finite group and character tables; real, pseudoreal, and complex representations; Weyl, Dirac, and Majorana equations; the expanding universe and group theory; grand unification; and much more The essential textbook for students and an invaluable resource for researchers Features a brief, self-contained treatment of linear algebra An online illustration package is available to professors Solutions manual (available only to professors)

Lie Groups and Lie Algebras for Physicists

Lie Groups and Lie Algebras for Physicists
Author: Ashok Das
Publisher: World Scientific Publishing Company
Total Pages: 0
Release: 2014-09-03
Genre: Lie algebras
ISBN: 9789814616904

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