Lie Algebras in Particle Physics (Frontiers in Physics)

Book Description

An exciting new edition of a classic text

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.

Customer Reviews:

classical.......2005-08-05

very well written text about the algebra of standard model,
but not for beginers,a very solid background in particle physics
and symmetry methods for physics is required

A good *first* start.......2003-08-14

This book is good for what it is, namely, something to get your feet wet. When learning the basics of particle physics, e.g. as an undergrad or a beginning experimentalist, this is the quickest way to get a feel for the standard model gauge group.
However, this is *not* a complete text on group theory in particle physics (and therefore, little of what you need for supersymmetric field theories and string theories). So in addition to this book, you'd need something else with an introduction to the other things you need for your particular interest. Try Gilmore's "Applications of Lie algebras...", which I believe is out of print (in libraries). Also, Cornwell's abridged "Group theory in physics" is good (though if you can find the older set of three volumes, that may be more suited to your desires).
I don't suggest many of the other books on group theory for particles/fields/strings. There are tidbits of group theory you can pick up in the particular text you are working with, e.g. "Quantum theory of Fields" by Weinberg if you are learning quantum field theory.
For mathematical physics in general, I strongly suggest "Gauge fields, knots, and gravity" (John Baez), "Differential Geometry for physicists" (Chris Isham), and "Mathematical Physics" (Geroch).

What do you need more?.......2003-02-11

I'd say that, at least, the Georgi's book is too underestimated here.

I agree that this book lacks some notions and concepts which are usually dealt with in the matmatical literature, but not on logical clearity. Every book has its own way. For example the later parts of Green, Schwarz and Witten are also a mere sketches but it sufficiently pinpoints every important steps. A physically inclined reader(?), soon realize that it is filled with (and you may feel the leakage of) the master's intuition. You can see what mathematics going on beneath the physics. It is a well-framed series of informal lectures which reveals some space-between-lines secret.

good supplement.......2002-03-09

good supplement of introductory quantum field theory. particle physics books often have aggressiveness but this is in a relaxed mood, apt for reading in fine sunday mornings. 27 chapters in 300 pages, short chapters, without one for manifold and topology. from this book you can't get a mathematically deep understanding of Lie algebra nor exotic viewpoint for particle/string, but that's not this is for. i hope someday this will be included in Dover classics.

1.finite groups 2.Lie groups 3.SU(2) 4.tensor operators 5.isospin 6.roots and weights 7.SU(3) 8.simple roots 9.more SU(3) 10.tensor methods 11.hypercharge and strangeness 12.Young tableaux 13.SU(n) 14.3-d harmonic oscillator 15.SU(6) and the quark model 16.color 17.constituent quarks 18.unified theories and SU(5) 19.classical groups 20.classification theorem 21.SO(2n+1)and spinors 22.SO(2n+2)spinors 23.SU(n) Mediocre.......2001-09-01

Georgi's book has its strengths and weaknesses. It is very strong on application to physics but suffers greatly from a lack of mathematical substance. It has all the earmarks of a mathematics book written by a physicist: lots of physical insight but poor logical structure. Clear definitions and statements of theorems are missing and contribute to the nebulous feel of the text.

This is the kind of book that a casual reader will go through and think he has learned alot but for which the serious student who seeks a precise, thorough understanding of the material will likely end up confused at many points. It is a book of tools. The reader will not obtain a mastery of the subject but must suppliment this book with other, more theoretical treatments of representation theory.

Book Description

This book shows how the well-known methods of angular momentum algebra can be extended to treat other Lie groups. Chapters cover isospin; the three-dimensional harmonic oscillator; algebras of operators that change the number of particles; permutations, bookkeeping, and Young diagrams; and more. 1966 edition.

Customer Reviews:

Top ten classical but nowadays incomplete review of group theory in Physics.......2007-03-20

The book of Lipkin has become a classical reference in group theoretical methods in physics, and is one of the most valuable reviews at the time of the establishment of the Gell-Mann-Ne'eman octet model. Divided into seven chapters and various later written appendixes, this work was originally thought as a comprehensive introduction to the unitary symmetry. This has been achieved in an impressive way, as shows the careful development of the topics and successive refinements. The su(3) symmetry is deduced naturally starting from the annihilation-creation operator formalism employed for the nucleon, and introducing the needed tools step by step. The (1966) more relevant groups SU(3), SU(4), SU(6) and SU(12) groups are analyzed in some detail, as well as some low rank symplectic groups and various subgroups intervening in the state labeling problem, such as the Wigner supermultiplet model. The author makes a self-contained presentation of the combinatorial technique of Young diagrams, which is inspired in the milestone work of M. Hammermesh, but presented here with astonishing simplicity to be applied by the reader without requiring a deep theoretical background.
A quite interesting section is devoted to the experimental predictions obtained from the octet model, like the classical example of the negative hyperon, discovered by Barnes et al. following the theoretical model. In all, this book shows the situation of the global internal symmetries in the 60s.
There is however one surprising fact about the book. In spite of the title, the concept of Lie group is nowhere defined adequately through the book. Although it is commonly understood that the group is meant when working with the corresponding Lie algebra, this can mislead some readers. Also the (informal) definition of Lie algebra given in equation (1.15) on page ten is false, or at least incomplete. A set of operators with some bracket (either of bosonic or fermionic type) defines a Lie algebra only if it is closed with respect to this brackets and additionally satisfies the Jacobi identity. None of this is found in the definition given in the book. To "satisfy commutation relations similar to those of angular momentum operators" is definitively not sufficient for higher rank algebras. I agree that this minor detail is irrelevant for the rest of the book, because the used operators obviously define a Lie algebra, but this can also lead to confusion, since apparently any arbitrary collection of operators would have the same property.

Although this book has aged quite well and remains an important reference, it is no more adequate for those who want an actualized overview of the classification of particles. There are obvious reasons for this, as the non-covered topics correspond to concepts or models that were developed later than the publication of the book. One example is the attribute color (around 1973), introduced to explain some remaining difficulties. This absence obviously extends to QCD (Quantum Chromodynamics). Also the unified theories and the model SU(5) of Georgi-Glashow (1974) are not covered, as well as the symmetry broken down from this group to the reductive group SU(3) x SU(2) x U(1), or the resulting proton decay. Such important absences, easily detected by the expert, are not immediate for the beginner. However, there is no doubt that this book is an excellent introduction to the specific problems of group theory applied to particle physics. In any case, in order to have a larger comprehension of the topic, the text must be completed with the reading of more modern or detailed monographs. Good complements to the book of Lipkin containing later developments and theories would be, for example, the work of Ne'eman [Symétries jauge et variétés de groupe, PUM, Montréal, 1979], the book of Georgi [Lie algebras in particle physics, Perseus Books, Reading, 1982] or the encyclopedic work of Cornwell [Group theory in physics, Academic Press, San Diego, 1984, volume 2].

I-spin, U-spin, V all spin for I-spin.......2004-11-14

This book is still a very useful resource, nearly four decades after it was first published.

And that's the case even if you aren't exactly a pedestrian. This is the Truth about Lie groups!

While this book is very readable as it takes you through isospin, SU(3), commutation rules, symmetry breaking, the three-dimensional harmonic oscillator, and creation and annihilation operators, the most valuable part is the use of Young diagrams to construct multiplets for SU(3), SU(4), SU(6), and SU(12).

That is, suppose you are taking a course on elementary particles. And you are using some standard text such as Halzen and Martin (also a book that has aged very well). Anyway, you get to page 62 or so and that book tells you that the best way to construct the SU(3) multiplets is to use Young tableaux. But that book doesn't tell you how to use them. This one does.

If you are learning about elementary particles, you can go through this book in a day or two. And you'll be glad you did.

Semi-Simple Lie Algebras and Their Representations (Dover Books on Mathematics)

Average customer rating:

A small book with a big Kernal
A practical guide to Lie algebras and representations
A pleasant read
A nice little summary of the theory

Semi-Simple Lie Algebras and Their Representations (Dover Books on Mathematics)
Robert N. Cahn
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

General | Science | Subjects | Books

ASIN: 0486449998

Book 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. Author Robert N. Cahn, who is affiliated with the Lawrence Berkeley National Laboratory in Berkeley, California, has provided a new preface for this edition. 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. 1984 ed.

Customer Reviews:

A small book with a big Kernal.......2006-12-30

I bought the book for Dynkin diagrams,
Cartan matrices and a better understanding of group theory
as it applies to Lie Algebras.
I got that so I'm satisfied with the book.
What I would like is a better coverage of the Standard theory and
ideas of symmetry breaking.
I also miss the connection to Weyl gauge theory and
the differential geometry involved.
Picky , Picky , Picky...
I think that Robert N. Cahn has done a very good job with this book
for price and content, but I can also see why
Europe is ahead of the USA in physics,
since it is not what is in the book,
but what is left out that troubles me.

A practical guide to Lie algebras and representations.......2003-11-03

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. There is no attempt to develop the theory formally, as done in usual textbooks on Lie algebras, but to present the material motivated by the rotation group SU(2), and also SU(3). The book is divided into sixteen sections. The first ten give a brief overview of the classification of semisimple algebras and their representations. For the proofs the reader is referred to the book of Jacobson [Lie algebras, Wiley 1962]. The purpose of this presentation is to introduce the concepts like Killing form, weights, root system, etc, using the examples of the two groups cited above, and then give the general description. Technical results are kept to a minimum, which causes a couple of omissions which are however used in later chapters [this is the case for the decomposition of any positive root as a sum of simple roots with integer positive coefficients]. The eleventh chapter introduces the Casimir operators of Lie algebras (more precisely the quadratic Casimir operator) and Freudenthal's formula for the dimension of weights spaces. In chapter 12 the Weyl group of a root system is discussed (but without commenting the Weyl chambers). Chapter XIII presents Weyl's formula for the dimension of irreducible representations, and illustrated with examples like sl(3) or the exceptional algebra of rank two. Chapter XIV begins with topics usually encountered in physical applications, like the decomposition of the tensor product of two irreducible representations. This and later chapters are strongly influenced by Dynkin's original work. In particular the theorem for the second highest representation is developed in detail. The last two chapters are devoted to the analysis of subalgebras of semisimple Lie algebras and the branching rules (i.e., decomposition of representations with respect to a certain subalgebra). The method based on the extension of the Dynkin diagrams is carefully developed, and the question of maximality of the subalgebra (regular or not) discussed. Here an extremely important observation is made, namely the existence of some little mistakes in the Dynkin's method (concerning the maximality of certain subalgebras in the exceptional case). This is pointed out with explicit exhibition of examples. The last chapter gives an insight into the branching rules, by the development of carefully chosen examples and the presentation of some results (without proof) due also to Dynkin.
Resuming, this book provides a quick introduction to the techniques and features of (finite dimensional) Lie algebras appearing in physical theories (e.g. the interacting boson model) without being forced to digest a formal mathematical development. Inspite of few points where the reader can get puzzled (due to the use of noncommented general properties), the text achieves its purpose and constitutes a valuable reference for physicists.

A pleasant read.......2003-03-01

Not only are Lie algebras interesting and important from a mathematical standpoint, an in-depth understanding of them is essential if one is to fully comprehend the physical theories of elementary particle interactions. All of these theories, from quantum field theories to string theories, to the current research on D-branes and M-theories, are dependent on the theory of Lie groups and Lie algebras. Because of its relaxed informal style, this book would be a good choice for the physics graduate student who intends to specialize in high energy physics. Those interested in mathematical rigor would probably want to select another text. Because of space restrictions, only the first thirteen chapters will be reviewed here.

In chapter 1 the author begins the study of SU(2), the group of unitary 2 x 2 matrices of determinant 1. He does this by first considering the matrix representations of infinitesimal rotations in 3-dimenensional space. "Exponentiating" these matrices gives the finite rotational matrices. He then shows that the consideration of products of finite rotations involves knowledge of the commutators of the infinitesimal rotations. Viewing these commutators abstractly motivates the definition of a Lie algebra. He then shows that the rotation matrices form a (3-dimensional) 'representation' of the Lie algebra. Higher-dimensional representations he shows can be obtained by analogies to what is done in quantum mechanics, via the addition of angular momentum and are parametrized by spin (denoted j). The representation of smallest dimension is given by j = 1/2 and corresponds to SU(2). He is careful to point out that the rotations in 3 dimensions and SU(2) have the same Lie algebra but are not the same group.

The constructions in chapter 1, particularly the concept of "exponentiating", are central to the understanding of Lie algebras in general. This is readily apparent in the next chapter wherein he studies the Lie algebra of SU(3), the 3x3 unitary matrices of determinant 1. SU(3) has to rank as one of the most important groups in elementary particle physics. The (abstract) Lie algebra corresponding to the commutation relations of this group have various representations, the 8-dimensional, or "adjoint" representation being one of great interest. The author finds the famous 'Cartan subalgebra' of the Lie algebra, shows that it 2-dimensional and Abelian, and how eigenvectors of the adjoint operator can form a basis for the Lie algebra, as long as this operator corrresponds to an element of the Cartan subalgebra. Further, he shows that the eigenvalues of this operator depend linearly on this element, and then defines functionals on the Cartan subalgebra, called the roots, and they form the dual space to the Lie algebra. Dual spaces are familiar to physicists in the Dirac bra-ket formalism.

The geometry of Lie algebras is very well understood and is formulated in terms of the roots of the algebra and a kind of scalar product (except is not positive definite) for the Lie algebra called the 'Killing form'. The Killing form is defined on the root space, and gives a correspondence between the Cartan subalgebra and its dual. The author then shows how to use the Killing form to obtain a scalar product on the root space, and this scalar product illustrates more clearly the symmetry of the Lie algebra. The property of being semisimple is then defined abstractly by the author, namely a Lie algebra with no Abelian ideals. He states, but does not prove entirely, that the Killing form is non-degenerate if and only if the Lie algebra is semisimple.

The treatment becomes more abstract in chapter 4, wherein the author studies the structure of simple Lie algebras, since every semisimple algebra can be written as the sum of simple Lie algebras. The author shows how to obtain the Cartan subalgebra in general, motivating his procedures with what is done for SU(3). He also proves the invariance of the Lie algebra and shows that it is the only invariant bilinear form on a simple Lie algebra. After a detour on properties of representations in chapter 5, wherein he constructs some useful relations for adjoint representations, the author uses these to again study the structure of simple Lie algebras in chapters 6 and 7. This involves the notion of positive and negative roots, and simple roots, and from the latter the author constructs the 'Cartan matrix', which summarizes 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). Their Dynkin diagrams are also constructed explicitly.

The author returns to representation theory in chapter 10, wherein he introduces the concept of a 'weight'. These come in sequences with successive weights differing by the roots of the Lie algebra. A finite dimensional irreducible representation has a highest weight, and each greatest weight is specified by a set of non-negative integers called 'Dynkin coefficients'. He then shows how to classify representations as 'fundamental' or 'basic', the later being ones where the Dynkin coefficients are all zero except for one entry.

In complete analogy with the theory of angular momenta in quantum mechanics, the author illustrates the role of Casimir operators in chapter 11. Freudenthal's recursion formula, which gives the dimension of the weight space, is used to derive Weyl's formula for the dimension of an irreducible representation in chapter 13. The reader can see clearly the power of the 'Weyl group' in exploiting the symmetries of representations.

A nice little summary of the theory.......1998-11-02

Very well written account of the theory, with almost all the necessary proofs to get familiar with the it. It's inspired by Jacobson's book, however a lot easier to read. It's out of print, but there is an online copy.

Lectures on Infinite-Dimensional Lie Algebra

Average customer rating:

Lectures on Infinite-Dimensional Lie Algebra
Minoru Wakimoto
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Paperback

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 9810241291

Group 21: Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras : Proceedings of the Xx1 International Colloquium on Group theoretica

Average customer rating:

Group 21: Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras : Proceedings of the Xx1 International Colloquium on Group theoretica
International Colloquium on Group Theoretical Methods in Physics 1996 , and H. D. Doebner
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

General | Physics | Science | Subjects | Books

Mathematical Physics | Physics | Science | Subjects | Books

Infinite Lie Algebras and Conformal Invariance in Condensed Matter and Particle Physics: Proc of the 10th John Hopkins Workshop on Current Problems

Average customer rating:

Infinite Lie Algebras and Conformal Invariance in Condensed Matter and Particle Physics: Proc of the 10th John Hopkins Workshop on Current Problems
V. Rittenberg
Manufacturer: World Scientific Pub Co Inc
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

Average customer rating:

Green functions from lie algebras
P Budini
Manufacturer: [International Centre for Theoretical Physics]
ProductGroup: Book
Binding: Unknown Binding

Integrable and non-integrable lie-algebra representations with applications to particle physics

Average customer rating:

Integrable and non-integrable lie-algebra representations with applications to particle physics
HaÌkan Snellman
Manufacturer: s.n.]
ProductGroup: Book
Binding: Unknown Binding

Quantum Theory | Physics | Science | Subjects | Books
ASIN: B0007B4EW2

Lie Algebras in Particle Physics. From Isospin to Unified Theories

Average customer rating:

Lie Algebras in Particle Physics. From Isospin to Unified Theories
Howard Georgi
Manufacturer: Perseus
ProductGroup: Book
Binding: Paperback
ASIN: B000LZFVJY

Simple lie algebras of rank 3 and symmetries of elementary particles in the strong interaction: Michiji Konuma, Kazuhisa Shima and Morihiro Wada (Progress of theoretical physics. Supplement :)

Average customer rating:

Simple lie algebras of rank 3 and symmetries of elementary particles in the strong interaction: Michiji Konuma, Kazuhisa Shima and Morihiro Wada (Progress of theoretical physics. Supplement :)
Michiji Konuma
Manufacturer: Research Institute for Fundamental Physics
ProductGroup: Book
Binding: Unknown Binding

Book Description

This digital document is an article from Renaissance Quarterly, published by Thomson Gale on September 22, 2006. The length of the article is 794 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: Francis Bacon and the Refiguring of Early Modern Thought: Essays to Commemorate the Advancement of Learning, 1605-2005.(Book review)
Author: Pete Langman
Publication: Renaissance Quarterly (Magazine/Journal)
Date: September 22, 2006
Publisher: Thomson Gale
Volume: 59 Issue: 3 Page: 939(3)

Article Type: Book review

Distributed by Thomson Gale

Books:

Books Index

Books Home

Recommended Books