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eBook Lie Groups, Lie Algebras, and Some of Their Applications (Dover Books on Mathematics) ePub

eBook Lie Groups, Lie Algebras, and Some of Their Applications (Dover Books on Mathematics) ePub

by Robert Gilmore

  • ISBN: 0486445291
  • Category: Mathematics
  • Subcategory: Math Science
  • Author: Robert Gilmore
  • Language: English
  • Publisher: Dover Publications (January 4, 2006)
  • Pages: 608
  • ePub book: 1448 kb
  • Fb2 book: 1494 kb
  • Other: lit mobi azw docx
  • Rating: 4.8
  • Votes: 607

Description

Lie group theory plays an increasingly important role in modern physical theories. Coauthors Jeanne and Robert Gilmore are married and live in Lafayette, Louisiana.

Lie group theory plays an increasingly important role in modern physical theories. Using the theory of Lie groups as a unifying vehicle, concepts and results from several fields of physics can be expressed in an extremely economical way. With rigor and clarity, this text introduces upper-level undergraduate students to Lie group theory and its physical applications. A music specialist, Robert Gilmore received his doctorate from Columbia University.

With rigor and clarity, this upper-level undergraduate text employs numerous exercises, solved problems, and figures to introduce upper-level undergraduates to Lie group theory and physical applications

With rigor and clarity, this upper-level undergraduate text employs numerous exercises, solved problems, and figures to introduce upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in expressing concepts and results from several fields of physics. Includes 75 figures and 17 tables.

Lie Algebras (Dover Books on Mathematics). Lie group theory plays an increasingly important role in modern physical theories

Lie Algebras (Dover Books on Mathematics). Lie group theory plays an increasingly important role in modern physical theories.

Download books for free. With rigor and clarity, this upper-level undergraduate text employs numerous exercises, solved problems, and figures to introduce upper-level undergraduates to Lie group theory and physical applications. Categories: Mathematics\Algebra.

Robert Gilmore: Lie Groups, Lie Algebras and Some of Their . 7 Lie Algebras and Root Spaces. I. General Structure Theory for Lie Algebras.

Robert Gilmore: Lie Groups, Lie Algebras and Some of Their Applications. II. The Secular Equation.

In fact, Lie groups enter physics primarily through their finite- and . The purpose of this book is to bridge the gap between those who do not know Lie group theory and those who do know.

In fact, Lie groups enter physics primarily through their finite- and matrix representations. Certain natural questions arise. The course covered Lie groups and algebras, representation theory, realizations and special functions, and physical applications. In this sense, this work fits between the books of Hamermesh and Helgason.

by Robert Gilmore First published February 8th 1974. Published January 4th 2006 by Dover Publications. Paperback, 608 pages. Author(s): Robert Gilmore. ISBN: 0486445291 (ISBN13: 9780486445298). Lie Groups Lie Algebras And Some Of Their Applications (Paperback). ISBN: 0486322564 (ISBN13: 9780486322568).

Автор: Gilmore, Robert Название: Lie Groups, Lie Algebras, and Some .

Using the theory of Lie groups as a unifying vehicle, concepts and results from several fields of physics can be expressed in an extremely economical way.

Download it once and read it on your Kindle device, PC, phones or tablets.

Lie groups, Lie algebras. There's no description for this book yet.

Lie groups, Lie algebras, and some of their applications. Are you sure you want to remove Lie groups, Lie algebras, and some of their applications from your list? Lie groups, Lie algebras, and some of their applications. Published 2005 by Dover Publications in Mineola, . Lie groups, Lie algebras. Includes bibliographical references and index. Originally published: New York : J. Wiley, 1974.

Lie group theory plays an increasingly important role in modern physical theories. Many of its calculations remain fundamentally unchanged from one field of physics to another, altering only in terms of symbols and the language. Using the theory of Lie groups as a unifying vehicle, concepts and results from several fields of physics can be expressed in an extremely economical way. With rigor and clarity, this text introduces upper-level undergraduate students to Lie group theory and its physical applications.An opening discussion of introductory concepts leads to explorations of the classical groups, continuous groups and Lie groups, and Lie groups and Lie algebras. Some simple but illuminating examples are followed by examinations of classical algebras, Lie algebras and root spaces, root spaces and Dynkin diagrams, real forms, and contractions and expansions. Reinforced by numerous exercises, solved problems, and figures, the text concludes with a bibliography and indexes.

Comments

Jogas Jogas
Simply put, I didn't like the book. It is too ambitious and this is bad for the reader, that can easily get lost amidst too many irrelevant details.

The author himself states in the preface of his newer book (R. Gilmore, "Lie Groups, Physics, and Geometry") that "Over the course of the years I realized that more than 90% of the most useful material in that book [the one being revised here] could be presented in less than 10% of the space." What else can I say?

The application-minded readers (e.g., physicists) will suffer from its style and contents, and the mathematician can find much better presentations elsewhere in the vast literature on the subject. So... who needs it? I enjoyed and profited much more from the book by B. G. Wybourne, "Classical Groups for Physicists."
Wymefw Wymefw
I'm really enjoying this text - several of my math books, as much as I love them, are so dense that at times I feel like I'm slogging through them. What I really appreciate about this book are the excellent figures and comprehensive summary tables; these are thoughtfully made and help solidify concepts and/or "big picture" ideas. I generally avoid books with too many words (I find that my style of learning leans towards equations, pictures, worked examples, and efficiently stated insights), and this text strikes just the right balance.
Arilak Arilak
It's a solid book. It covers both mathematical subtleties and physical applications. It's written at a very advanced level.

However, a warning to the uninitiated: He is sloppy with his notation. It's rarely explained or made precise. You sort of have to unravel what the hell he is trying to say. For example, he heavily relies on Einsteinian notation in his presentation on covariance, contravariance and metrics, but I don't think he ever mentions he is using it. If you are not already very familiar with the types of conventions that he chooses to use, you will find that the notation quickly interferes with grasping the material. I often found that the hardest part of understanding his explanations was understanding how he was using notation. I understand that he is using professional language, but when that becomes the biggest obstacle in understanding the material, perhaps there is a better way of doing it. In this sense, I wish he was more of a mathematician.
Pedar Pedar
I haven't read this whole book cover to cover, because of time constraints. However, I can say that it is extremely clear in it's exposition. The material is very well chosen for use by physicists. I have read pure math books on this topic, and while they can be more sophisticated and thorough, they are rarely as straight forward, nor do they cover the breadth of material in this book.

In sum I would have to agree with what I was told: "this is the book on Lie Algebra for a physicist".
Rose Of Winds Rose Of Winds
Surely the subject matter of Lie Algebras must be more than difficult if there exist Schaum Outlines even about Tensor Theory (see e.g. Kay, Tensor Calculus), but NOT about Lie Algebras. Nevertheless, Gilmore manages to mess up things quite completely.
Besides, what's the point of requesting such an inordinate amount of prerequisites? It's like saying: "I'll explain you Differential Geometry, but you must already know Quantum Physics, Lagrangian Mechanics, Algebraic Topology, Tensor Theory, Measure Theory, General Relativity and Cosmology" (so to speak). Thanks, prof. Gilmore, had I had such a background, I'd teach YOU how to write a DECENT paper on Lie Algebras.
Being not yet convinced, you should compare Gilmore's rambling exposition with a gem of graduate-level divulgative literature (although concerning the different topic of functional analysis): Infinite Dimensional Analysis, A Hitchhiker's guide, of Aliprantis and Border. Over 600 crystal-clear and extremely rigorous pages teaching everything you need to know about Measure Theory, Advanced Topology, Riesz Spaces and much more.
Gilmore's book has a number of unpleasant features, among which the constant mixing up of the complex case with the real one. Exposition jumps ceaselessly from linear vector functions on the real field to sesquilinear functions on the complex field, from orthogonal matrices to unitary matrices and so on and on.
Here are some precious samples picked from the first 100 pages:
Page 28: tensor notation (the ill-famed tensor product symbol "⊗") is abruptly introduced without any previous explanation, together with such inspired mystical definitions as "a tensor is a vector". Gilmore then goes on happily this way for three more pages, with the result you might imagine.
Page 69: a (n)hasty exposition of "Some realization for a continuous group of transformations", barely a page long, leaving more doubts than elucidations.
Page 78: The author begins speaking of Sigma-Algebras and μ-Integrals, terms typical of measure theory, without any previous warning. You baffled? Come on! Isn't it true that even children know about measure theory, Lebesgue integrals, Sigma Algebras and Measurable Functions?
That was enough for me. I didn't read farther. As soon as I reached page 100 I gave up. Next thing I ran a search of a reimboursement clause throughout the book. Too bad I found none. I could have started a lawsuit. Next after that, I bought online the excellent book of Hall, Lie Groups, Lie Algebras and Representations, edited by Springer-Verlag, that I am currently and profitably reading.
Thanks, prof. Gilmore, for a waste of money (29,95 USD) and several tens of unprofitable hours (plus thirty minutes to write and post this review).
ALAN ALAN
GOD BE NEEDED TO UNDERSTAND THIS BOOK, NO SHOWS ARE THE PREREQUISITES, A CHAOS IN THE ORGANIZATION, NOT UNDERSTAND THIS BOOK FOR NOTHING, IS THE MYSTERY OF THE HOLY TRINITY, ONLY WHEN DIE AND BE SPIRIT MAY UNDERSTAND THE VERY BAD BOOK.