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
Publisher : Oxford University Press
ISBN 13 : 0199662924
Total Pages : 216 pages
Book Rating : 4.1/5 (996 download)

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Book Synopsis Lie Groups and Lie Algebras - A Physicist's Perspective by : Adam M. Bincer

Download or read book Lie Groups and Lie Algebras - A Physicist's Perspective written by Adam M. Bincer and published by Oxford University Press. This book was released on 2013 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Das Ashok
Publisher : World Scientific
ISBN 13 : 9814603295
Total Pages : 360 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Lie Groups And Lie Algebras For Physicists by : Das Ashok

Download or read book Lie Groups And Lie Algebras For Physicists written by Das Ashok and published by World Scientific. This book was released on 2014-09-03 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Groups, Physics, and Geometry

Author : Robert Gilmore
Publisher : Cambridge University Press
ISBN 13 : 113946907X
Total Pages : 5 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Lie Groups, Physics, and Geometry by : Robert Gilmore

Download or read book Lie Groups, Physics, and Geometry written by Robert Gilmore and published by Cambridge University Press. This book was released on 2008-01-17 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Algebras with Applications to Physics, Geometry, and Mechanics

Author : D.H. Sattinger
Publisher : Springer Science & Business Media
ISBN 13 : 1475719108
Total Pages : 218 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics by : D.H. Sattinger

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.

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

Author : Josi A. de Azcárraga
Publisher : Cambridge University Press
ISBN 13 : 9780521597005
Total Pages : 480 pages
Book Rating : 4.5/5 (97 download)

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Book Synopsis Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics by : Josi A. de Azcárraga

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.

Differential Geometry and Lie Groups for Physicists

Author : Marián Fecko
Publisher : Cambridge University Press
ISBN 13 : 1139458035
Total Pages : 11 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Differential Geometry and Lie Groups for Physicists by : Marián Fecko

Download or read book Differential Geometry and Lie Groups for Physicists written by Marián Fecko and published by Cambridge University Press. This book was released on 2006-10-12 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, and Representations

Author : Brian C. Hall
Publisher : Springer Science & Business Media
ISBN 13 : 9780387401225
Total Pages : 376 pages
Book Rating : 4.4/5 (12 download)

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Book Synopsis Lie Groups, Lie Algebras, and Representations by : Brian C. Hall

Download or read book Lie Groups, Lie Algebras, and Representations written by Brian C. Hall and published by Springer Science & Business Media. This book was released on 2003-08-07 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics. Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it a useful addition to the literature. First, it treats Lie groups (not just Lie alge bras) in a way that minimizes the amount of manifold theory needed. Thus, I neither assume a prior course on differentiable manifolds nor provide a con densed such course in the beginning chapters. Second, this book provides a gentle introduction to the machinery of semi simple groups and Lie algebras by treating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory. The standard books on Lie theory begin immediately with the general case: a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. This approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time.

Lie Groups, Lie Algebras, and Some of Their Applications

Author : Robert Gilmore
Publisher : Courier Corporation
ISBN 13 : 0486131564
Total Pages : 610 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Lie Groups, Lie Algebras, and Some of Their Applications by : Robert Gilmore

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.

Group Theory in a Nutshell for Physicists

Author : A. Zee
Publisher : Princeton University Press
ISBN 13 : 1400881188
Total Pages : 632 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Group Theory in a Nutshell for Physicists by : A. Zee

Download or read book Group Theory in a Nutshell for Physicists written by A. Zee and published by Princeton University Press. This book was released on 2016-03-29 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 for Physicists

Author : Robert Hermann
Publisher :
ISBN 13 :
Total Pages : 216 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Lie Groups for Physicists by : Robert Hermann

Download or read book Lie Groups for Physicists written by Robert Hermann and published by . This book was released on 1966 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lie Algebras In Particle Physics

Author : Howard Georgi
Publisher : CRC Press
ISBN 13 : 0429967764
Total Pages : 340 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Lie Algebras In Particle Physics by : Howard Georgi

Download or read book Lie Algebras In Particle Physics written by Howard Georgi and published by CRC Press. This book was released on 2018-05-04 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the author convinces that Sir Arthur Stanley Eddington had things a little bit wrong, as least as far as physics is concerned. He explores the theory of groups and Lie algebras and their representations to use group representations as labor-saving tools.

Lie Algebras and Applications

Author : Francesco Iachello
Publisher : Springer
ISBN 13 : 3540362398
Total Pages : 196 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Lie Algebras and Applications by : Francesco Iachello

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.

Lie Groups

Author : Claudio Procesi
Publisher : Springer Science & Business Media
ISBN 13 : 0387289291
Total Pages : 616 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Lie Groups by : Claudio Procesi

Download or read book Lie Groups written by Claudio Procesi and published by Springer Science & Business Media. This book was released on 2007-10-17 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Lie Groups and Lie Algebras

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
ISBN 13 : 0521889693
Total Pages : 237 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis An Introduction to Lie Groups and Lie Algebras by : Alexander A. Kirillov

Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples

Quantum Mechanics Via Lie Algebras

Author : Arnold Neumaier
Publisher :
ISBN 13 : 9783110406108
Total Pages : 500 pages
Book Rating : 4.4/5 (61 download)

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Book Synopsis Quantum Mechanics Via Lie Algebras by : Arnold Neumaier

Download or read book Quantum Mechanics Via Lie Algebras written by Arnold Neumaier and published by . This book was released on 2020-10-04 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lie Groups

Author : J.J. Duistermaat
Publisher : Springer Science & Business Media
ISBN 13 : 3642569366
Total Pages : 352 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Lie Groups by : J.J. Duistermaat

Download or read book Lie Groups written by J.J. Duistermaat and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This (post) graduate text gives a broad introduction to Lie groups and algebras with an emphasis on differential geometrical methods. It analyzes the structure of compact Lie groups in terms of the action of the group on itself by conjugation, culminating in the classification of the representations of compact Lie groups and their realization as sections of holomorphic line bundles over flag manifolds. Appendices provide background reviews.

Notes on Lie Algebras

Author : Hans Samelson
Publisher : Springer Science & Business Media
ISBN 13 : 1461390141
Total Pages : 172 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Notes on Lie Algebras by : Hans Samelson

Download or read book Notes on Lie Algebras written by Hans Samelson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Cartan sub Lie algebra, roots, Weyl group, Dynkin diagram, . . . ) and the classification, as found by Killing and Cartan (the list of all semisimple Lie algebras consists of (1) the special- linear ones, i. e. all matrices (of any fixed dimension) with trace 0, (2) the orthogonal ones, i. e. all skewsymmetric ma trices (of any fixed dimension), (3) the symplectic ones, i. e. all matrices M (of any fixed even dimension) that satisfy M J = - J MT with a certain non-degenerate skewsymmetric matrix J, and (4) five special Lie algebras G2, F , E , E , E , of dimensions 14,52,78,133,248, the "exceptional Lie 4 6 7 s algebras" , that just somehow appear in the process). There is also a discus sion of the compact form and other real forms of a (complex) semisimple Lie algebra, and a section on automorphisms. The third chapter brings the theory of the finite dimensional representations of a semisimple Lie alge bra, with the highest or extreme weight as central notion. The proof for the existence of representations is an ad hoc version of the present standard proof, but avoids explicit use of the Poincare-Birkhoff-Witt theorem. Complete reducibility is proved, as usual, with J. H. C. Whitehead's proof (the first proof, by H. Weyl, was analytical-topological and used the exis tence of a compact form of the group in question). Then come H.