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

The four real division algebras (reals, complexes, quaternions and octonions) are the most obvious signposts to a rich and intricate realm of select and beautiful mathematical structures. Using the new tool of adjoint division algebras, with respect to which the division algebras themselves appear in the role of spinor spaces, some of these structures are developed, including parallelizable spheres, exceptional Lie groups, and triality. In the case of triality the use of adjoint octonions greatly simplifies its investigation. Motivating this work, however, is a strong conviction that the design of our physical reality arises from this select mathematical realm. A compelling case for that conviction is presented, a derivation of the standard model of leptons and quarks.
The book will be of particular interest to particle and high energy theorists, and to applied mathematicians.

Customer Reviews:

I am waiting for Dixon 's Octonians..........2007-02-10

I have not yet received my command. P. MERAT

Mathematics behind physics.......1997-09-29

This is an excellent book for those who want to study Hamilton's quaternions, and other algebraic structures, used in modern physics. Dixon believes that octonions and triality of Spin(8) are essential in understanding particle physics. This clear exposition contains many ideas which have gone unnoticed from other researchers. The book is a treasure trove for mathematical physicists. The author also compares the Cayley algebra of octonions to other algebraic systems used in physics: matrices and Clifford algebras, in particular the Dirac algebra.

Groups and Symmetry: A Guide to Discovering Mathematics (Mathematical World, Vol. 5) (Mathematical World)

Average customer rating:

the best math textbook I've ever had
An excellent primer on abstract algebra

Groups and Symmetry: A Guide to Discovering Mathematics (Mathematical World, Vol. 5) (Mathematical World)
David W. Farmer
Manufacturer: American Mathematical Society
ProductGroup: Book
Binding: Paperback

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Symmetry
The Shape of Space (Pure and Applied Mathematics)

ASIN: 0821804502

Book Description

In most mathematics textbooks, the most exciting part of mathematics--the process of invention and discovery--is completely hidden from the reader. The aim of Groups and Symmetry is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: Its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you.

Suitable for a one-semester course at the beginning undergraduate level, there are no prerequisites for understanding the text. Any college student interested in discovering the beauty of mathematics will enjoy a course taught from this book. The book has also been used successfully with nonscience students who want to fulfill a science requirement.

Customer Reviews:

the best math textbook I've ever had.......2006-02-10

This book was the foundational textbook for a 100-level class in symmetry at my university. I recommend it highly to anyone who wants to get a better feel for what mathematicians actually do and think about and work with. Folks who never got into the higher math classes often have a different idea of what mathematics is all about than mathematicians. At the level of introductory algebra and geometry and even some calculus, math education often seems to be mainly about memorizing formulas and recognizing in which situations to apply them. That's an important thing to learn, but it is not useful for imparting an idea and a feel of the field of mathematics as a whole. Farmer's book brings home the understanding that mathematics is, at its heart, about patterns and that mathematics is not so much about memorization and application as it is about discovery.

The level of mathematical understanding required to get something useful out of this book is low. I believe the professor required beginning algebra as the prerequisite. If you can count to six, recognize the difference between a square and a pentagon, and understand that variables like n, m, or x can be used as substitutes for numbers then you probably have enough mathematical sophistication to work your way through this book and gain insights into the beauty of higher math.

An excellent primer on abstract algebra.......2002-09-23

Groups are the first structures encountered in abstract algebra and form the foundation for most of the others. Fortunately, they are also the easiest to physically represent, so in some sense they are the most concrete. In this book, groups are introduced as the motions and structures of geometric figures, so the presentation is largely by diagram rather than formula. Very little previous knowledge of mathematics is required and after reading the book, you will have a solid understanding of what a group is.
The first topic is the moving of a complete figure to a different location of the plane defined by a grid of points. By keeping the figure rigid and fixed in orientation, a set of legal moves is defined. After that, some of the rules are relaxed and that allows for additional moves to be added. Exercises and problems are put forward here and throughout the book, and with the accent on figures, often give the appearance of a game.
The next steps are then to allow for all possible rotations, translations and reflections of the objects, using these to explain the structure of a group. This is an effective way to introduce group theory, and is how I will do it if I teach abstract algebra again. Permutation and plane tiling symmetry groups are then introduced and examined, and their relationship to the previous groups discussed, which introduces the concept of isomorphism.
Basic group theory is something that everyone can understand, as humans have a natural affinity for patterns and recognizing them despite "trivial" alterations. This book is an excellent primer on group theory and I strongly recommend it to anyone either learning or teaching abstract algebra.

Published in Journal of Recreational Mathematics, reprinted with permission.

The Theory of Groups and Quantum Mechanics
Average customer rating:

one the the most important work in quantum mechanics

Still a good book

A wonderful book

One of the two great classics on group theory in physics

Classic from the early days of quantum mechanics

The Theory of Groups and Quantum Mechanics
Hermann Weyl
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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Symmetry

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Group Theory and Its Application to Physical Problems (Dover Books on Physics and Chemistry)

ASIN: 0486602699

Book Description

This landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves — rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric transformations.

Customer Reviews:

one the the most important work in quantum mechanics.......2006-02-22

It's a very important book, written by the father of group theory application in physics (with Wigner and Pauli), and one of the best mathematician of 20th century, Hermann Weyl. Everyone who wants study a deeper view of quantum mechanics, in his intrinsic mathematical formulation, should read this work. After a firt brief introduction to quantum theory, he passes to explain the theory of rapresentation of groups, and its physical application, like the rotation group, or Lorentz group, and finally the theory of simmetry. It's a fundamental book for a good understandig of the importance of simmetries in modern physics. Without any doubt one the the most important work in quantum mechanics.

Still a good book.......2003-02-27

Written in the early years of the quantum theory, the author of this book foresaw the importance of considering symmetry in physics, the use of which now pervades most of theoretical high energy physics. Indeed, with the advent of gauge theories, and their experimental validation, it is readily apparent that symmetry principles are here to stay, and are just not accidental curiosities. A reader of the book can still gain a lot from the perusal of this book, in spite of its date of publication and its somewhat antiquated notation. Older books also have the advantage of discussing the material more in-depth, and do not hesitate to use hand-waving geometrical pictures when appropriate. This approach results in greater insight into the subject, and when coupled with eventual mathematical rigor gives it a solid foundation. One example where the discussion is superior to modern texts is in the author's discussion of group characters and their application to irreducible representations and spectra in atomic systems.

The reader will no doubt probably want to couple the reading of this book with a more modern text so as to alleviate the notational oddities in this book. The author's presentation is clear enough though to make an appropriate translation to modern notation. The reader will then be well prepared to tackle more advanced material in mathematical and theoretical physics that make use of the group-theoretic constructions that take place in this book.

A wonderful book.......2001-11-08

This is my favorite introduction to quantum mechanics. It is a difficult book, because it is succinct, though clear, and reflects Weyl's powerful intellect and original approach at every step. Each page is a challenge, but worth the effort.

One of the two great classics on group theory in physics.......2001-02-18

The other one is Wigner's "Group Theory and Quantum Mechanics". As it is true of the other great books by Weyl, this is not an easy book, but it is, by all means, accessible. Don't try to read it in front of the TV set. Get pencil and paper, put yourself in a calm and contemplative mood and patiently read the words of the master. Hermann Weyl, one of the great minds of the 20th century, wrote this book with utmost care to make it self-contained. Sometimes you have to be deep in order to be brief, so the book requires some thought. But the main ideas are all there, and the connection of group theory with quantum mechanics has here its best treatment, in my humble opinion. But in less humble too: this was the only book concerning physics which Enrico Fermi read as a grown up. Once, Max Born had to write a synthetic exposition of Quantum Mechanics. After he finished it, he saw, for the first time, this book, and Weyl's synthesis of QM. He felt depressed by the superiority of Weyl's text. The book was originally written in German, but the translation is excellent, due to the great American cosmologist H. P. Robertson, of Robertson-Walker fame.

Classic from the early days of quantum mechanics.......2000-06-27

Although published by Dover in 1984, this book dates back to about 1930, when Weyl was the big proponent of group theory in quantum mechanics. Because of this date, much of what modern books on group theory would include, is absent from the book. It mainly discusses the permutation group. The book is, however, of historic interest, as Weyl (mathematician) tried to convince the physicists to exploit group theory - which even gave rise to some irritation ("group pest").

Average customer rating:

FIRST read a book in Lie groups

Quantum Mechanics: Symmetries
Walter Greiner , and Berndt Müller
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 3540580808

Book Description

Quantum Mechanics (Symmetries) deals with a particularly appealing and successful concept in advanced quantum mechanics. After a brief introduction to symmetries in classical mechanics, the text turns to their relevance in quantum mechanics, the consequences of rotation symmetry, and the general theory of Lie groups. The isospin group, hypercharge, SU(3) and their applications are all dealt with in depth before chapters on charm, SU(4), and dynamical symmetries lead to the frontiers of research in particle physics. This unique text comprises more than 120 detailed, worked examples and problems.As the third reprint of the second edition, this book has been revised to bring the text up to date.

Customer Reviews:

FIRST read a book in Lie groups.......2003-08-15

Book: Quantum Mechanics - Symmetries, 2nd edition, 15 chapters, 496 pages

Scope of the book: applications of group theory in elementary particle physic (no field theory!)

Reader: PhD student in physics, I am a beginner in that area, this is my first book in symmetries and Lie groups.

My evaluation:
The math sections in the book give u some basic notion of Lie groups but are NOT sufficient to fully understand the logic behind the scene everywhere. My advice is to read some good book in Lie groups in advance.
The strongest feature of the book is its richnes of examples and solved exercises both in group theory and in its application to particle physics. You can learn a lot of analytical 'tricks' from the solutions.
At the same time the text is full of small errors (signs, indeces, equation numbers, misprints). They are easy to detect and fun to debug and keep you concentrated while debugging.
My main objection is that very often the logic in the text remains hidden, broken or fuzzy. Sometimes they prove some statement but at the end you can't tell what was actually proven or under what conditions that proof is valid, what facts it is derived from, does it rely on implicit assumptions or it's generaly true. As a consequence of that you are not sure if you can apply the statement for a situation that is not exactly the one discussed in the book. Sometimes it's hard to tell if they are talking about a necessary of sufficient condition or both. Or they, having something in mind that you don't know about, make some sudden assumption and you wonder why. Some concepts are not defined sharply from the begining but instead the authors use fussy definitions and define them much later (example: tensor product of multiplets and its reduction is defined understandably in chapter 10 but is used all the time before that). The explanations of the algebra in the examples and exercises is also not the best since in many cases I see a more logical, organized and understandable way to explain it to the reader. Also in some cases the book gives just the algebra without giving the reader the more fundamental cause for some fact(example: in exercise 8.3 page 255 they have two matrices connected by a similarity transformation, they prove with some algebra that the eigenvalues remain the same but don't tell you that's always the case with similarity transformations).

To my opinion the authors have to a lot of work to do to make the logic fully explicit and understandable to the reader everywhere in the text. Without that, the book can be regarded as a nice collection of solved examples and exercises in group theory and particle physics.

I give that book 3 out of 5 stars and hope that the other volumes of the sequence don't have that flaw.

Contents of the book:

chap1: symmetries in classical physics, Noether's theorem, symmetries in quantum mechanics and their generators: momentum, angular momentum, energy and spin operators

Book Description

This book is a detailed reference on Lie algebras and Lie superalgebras presented in the form of a dictionary. It is intended to be useful to mathematical and theoretical physicists, from the level of the graduate student upwards. The Dictionary will serve as the reference of choice for practitioners and students alike.

Key Features:
* Compiles and presents material currently scattered throughout numerous textbooks and specialist journal articles
* Dictionary format provides an easy to use reference on the essential topics concerning Lie algebras and Lie superalgebras
* Covers the structure of Lie algebras and Lie superalgebras and their finite dimensional representation theory
* Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras

Quantum Mechanics: Symmetries (Greiner, Walter//Theoretical Physics 2nd Corr ed)

Average customer rating:

A great companion book for learning Group Therory in Quantum Mechanics
read a Lie groups math book FIRST
quantum mechanics symmetries
QM for advanced larner.
full of useful mathematical tools.

Quantum Mechanics: Symmetries (Greiner, Walter//Theoretical Physics 2nd Corr ed)
Walter Greiner , and Berndt Muller
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Book Description

Quantum Mechanics - Symmetries deals with a particularly appealing and successful concept in advanced quantum mechanics. After a brief introduction to symmetries in classical mechanics, the text turns to their relevance in quantum mechanics, the consequences of rotation symmetry, and the general theory of Lie groups. The isospin group, hypercharge, SU(3), and their applications are all dealt with in depth before chapters on charm, SU(4), and dynamical symmetries lead to the frontiers of research in particle physics. This unique text comprises more than 120 detailed, worked examples and problems. This second edition has been corrected and is presented in both a new attractive cover and a new format. In addition, some new examples and exercises have been included.

Customer Reviews:

A great companion book for learning Group Therory in Quantum Mechanics.......2007-07-10

When learning Quantum Mechanics (QM) you sooner or later just have to learn Group Theory.
There is no escape. The more advanced QM the more Group Theory there will be.

This book is "Group Theory in Action"!

However, my experience is that it is practically impossible to fully appreciate the ideas
of Group Theory from any physics text, including this one - even though it's entirely devoted
to the subject.

If you are new to the subject of groups, my advice is this:
1.) Read first an elementary text on Finite Groups.
Chapter 10 in the book Mathematics of Classical and Quantum Physics will do the job nicely and,
besides, you will own a book that covers a lot of the mathematics of QM.

2.) Read Greiners book in conjunction with a book on Matrix Lie Groups and Representation Theory.
The limitation to Matrix Lie Groups as opposed to General Lie Groups) is in the context of Greiners
book not a limitation at all. I strongly recommend the text Lie Groups, Lie Algebras, and Representations: An Elementary Introduction.
If you buy a more advanced text there will be prerequisites such as knowledge of Manifold Theory.

3.) Be aware of the following traps:
i.) As other reviewers have pointed out there are many small errors in the book, mostly typos.
There are also some bigger errors. For instance, the groups SU(2) and SO(3) are NOT isomorphic
as is stated in several places. (There is a 2:1 correspondence, i.e. a homomorphism and their
respective algebras are isomorphic.)

ii.) The book is not well organized in the sense that methods and concepts are used long before
they are properly defined. This is precicely why you should have a companion math text to go along
with it.

iii.) There is a constant change of notation in that quantities are defined in one way and given
a name and then, in the next paragraph a new name is introduced for a quantity that differs only
by a constant factor from the previous definition. This goes on and on and on and will be
confusing at first.

iv.) As in most physics texts there is a constant confusion as to what is what.
Groups and their respective Algebras are given the same name. One has to extract from the context what is meant.
Representations of groups and algebras, i.e. matrices (operators in the vector spaces of QM),
are confused with the invariant irreducible subspaces of the vector spaces on which the representations act.
This is something one has to get used to. It is the same in most physics texts and even in some math texts.

/********************/
Apart from these flaws, the book is fantastic. Just as it is hard to learn Group Theory from a
physics text alone, it's quite hard to learn Group Theory from a math text alone because typically,
there are very few solved problems to see the theory in action.

Therefore I recommend this book for students of mathematics as well as physics.

read a Lie groups math book FIRST.......2003-08-25

Book: Quantum Mechanics - Symmetries, 2nd edition, 15 chapters, 496 pages

Scope of the book: applications of group theory in elementary particle physic (no field theory!)

Reader: PhD student in physics, I am a beginner in that area, this is my first book in symmetries and Lie groups.

My evaluation:
The math sections in the book give u some basic notion of Lie groups but are NOT sufficient to fully understand the logic behind the scene everywhere. My advice is to read some good book in Lie groups in advance.
The strongest feature of the book is its richnes of examples and solved exercises both in group theory and in its application to particle physics. You can learn a lot of analytical 'tricks' from the solutions.
At the same time the text is full of small errors (signs, indexes, equation numbers, misprints). They are easy to detect and fun to debug and keep you concentrated while debugging.
My main objection is that very often the logic in the text remains hidden, broken or fuzzy. Sometimes they prove some statement but at the end you can't tell what was actually proven or under what conditions that proof is valid, what facts it is derived from, does it rely on implicit assumptions or it's generaly true. As a consequence of that you are not sure if you can apply the statement for a situation that is not exactly the one discussed in the book. Sometimes it's hard to tell if they are talking about a necessary of sufficient condition or both. Or they, having something in mind that you don't know about, make some sudden assumption and you wonder why (example: equation (13.3) on page 442 assumes that the parity transformed wave function is proportional to the old one. why? cause they assume implicitly without stating it that parity commutes with the Hamiltonian, hence they have common eigenfunctions). Some concepts are not defined sharply from the begining but instead the authors use fussy definitions and define them much later (example: tensor product of multiplets and its reduction is defined understandably in chapter 10 but is used all the time before that). The explanations of the algebra in the examples and exercises is also not the best since in many cases I see a more logical, organized and understandable way to explain it to the reader. Also in some cases the book gives just the algebra without giving the reader the more fundamental cause for some fact(example: in exercise 8.3 page 255 they have two matrices connected by a similarity transformation, they prove with some algebra that the eigenvalues remain the same but don't tell you that's always the case with similarity transformations).

To my opinion the authors have to a lot of work to do to make the logic structure of the text (the connections between different statements,the difference between assumptions and derivable facts) fully explicit and understandable to the reader everywhere in the text. Without that, the book can be regarded as a nice collection of solved examples and exercises in group theory and particle physics.

I give that book 3 out of 5 stars and hope that the other volumes of the sequence don't have that flaw.

Contents of the book:

chap1: symmetries in classical physics, Noether's theorem, symmetries in quantum mechanics and their generators: momentum, angular momentum, energy and spin operators

chap2: angular momentum algebra; irreducible representations of SO(3); addition of angular momenta; Clebsh-Gordon coefficients

chap3: Lie groups, generators, Lie algebra; Casimir operators and Racah theorem; multiplets;

chap4: enumeration of the multiplets through eigenvalues of Casimir operators; energy degeneracy within a multiplet; two or more commuting symmety groups

chap5: neutron, proton doublet; isospin SU(2) symmetry; pion triplet; adjoint representation of Lie algebra

chap6: charge Q; hypercharge Y; baryons, antibaryons, baryon resonances; T3-Y diagrams;

chap7: U(n) and SU(n) groups; generators, Lie algebra of SU(3); subalgebras of SU(3) and shift operators; dimensions of SU(3) multiplets D(p,q);

chap8: smallest non-trivial representations of SU(3), quarks; meson multiplets; tensor product of multiplets and their reduction; Gell-Mann-Okubo mass formula; quark models with spin added, SU(6); wave functions construction, proton, neutron, baryon decuplet, baryon octet; mass formula in SU(6);

chap9: permutation group Sn, identical particles; Young diagrams; dimensions of irreducible Sn representations; connection to SU(n) multiplets; dimensions of SU(n); decompositions of SU(n) multiplet into SU(n-1) multiplets; decomposition of tensor product of multiplets with Young diagrams;

chap10: group characters; schur first and second lemma; orthogonality relations of characters of discrete finite groups; reduction of reducible representations; continuous, compact groups, group integration; integration over unitary groups; group characters of U(n); quark-gluon plasma example;

chap11: charm, SU(4), group generators; smallest non-trivial representations of SU(4), [4] and [4bar]; decomposition of tensor products of SU(4) multiplets; OZI rule for suppressing reactions; meson and baryon multiplets, SU(3) content; potential model of charmonium;SU(4)[with spin SU(8)] mass formula;

chap12: weight operators, standard Cartan-Weyl basis of a semi-simple Lie algebra; root vectors; graphic representations of root vectors and Lie algebras; simple roots and Dynkin diagrams;

chap13: space reflection (parity); time reversal; antilinear operators, complex conjugate operator K, antiunitary operator; general form of time reversal operator in coordinate representation for particle with spin;

chap14: classical hygrogen atom constants of motion: energy, angular momentum, Runge-Lenz vector; corresponding quantum constants of motion (operators), their algebra and group SO(4)- dynamical symmetry; decoupling of the SO(4) algebra into two SO(3) algebras and determination of the energy eigenvalues (Pauli method i guess); classical and quantum isotropic oscillator;

chap15: compact and noncompact Lie groups; group SU(p,q); group SO(p,q); generators of SO(2,1), infinitesimal operators, Casimir operators; non-compactness of SO(2,1) and its infinite dimensional irreducible unitary representations; application of SO(2,1) representations to scattering problems;

quantum mechanics symmetries.......2000-07-27

This is the most stupid book that I have ever seen. The main concepts of Elementary Particles Theory are introduced before the Quantum Field Theory has been developed. Without knowing Dirac's equation how on the Earth is possible to grasp the intricasies of Modern Physics? Lee groups are not introduces properly either -- the level of mathematical discussion is very low. For all of you who wants to use comprehensive series on Modern Physics I recommend the old ones by Landau and Lifshitz.

QM for advanced larner........2000-02-22

Probably for most of the people it is better to start QM with easier books, e.g., Landou. Greiner's physics series are little more sophisticated, and may be difficult for someone with poor math background. For someone who has strong math background, Greiner's books are fun to read even without any physics background. With your strong math background, you can learn a lot out of this text.

full of useful mathematical tools........2000-02-20

this volume is not only useful for understanding non-relativistic quantum mechanics but also it is filled with mathematical tools that is useful in many science and engineering analysis. symmetry of the operators plays always an important role in simplifying the analysis of formidable coupled equations. i found this volume very useful in many ways.

Groups and Symmetry (Undergraduate Texts in Mathematics)

Average customer rating:

Excellent introduction to abstract algebra through group theory
Excellent introduction to group theory
interesting format

Groups and Symmetry (Undergraduate Texts in Mathematics)
M. A. Armstrong
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387966757

Book Description

Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal style, the material is divided into short sections, each of which deals with an important result or a new idea. Throughout the book, emphasis is placed on concrete examples, often geometrical in nature, so that finite rotation groups and the 17 wallpaper groups are treated in detail alongside theoretical results such as Lagrange's theorem, the Sylow theorems, and the classification theorem for finitely generated abelian groups. A novel feature at this level is a proof of the Nielsen-Schreier theorem, using groups actions on trees. There are more than 300 exercises and approximately 60 illustrations to help develop the student's intuition.

Customer Reviews:

Excellent introduction to abstract algebra through group theory.......2005-09-14

This was the textbook for my first course in abstract algebra and the first "yellow book" that I read. I found it an excellent book: rather than starting with axioms and dryly deriving everything, it gets one to contemplate the meaning and motivation behind the axioms. This book will encourage you to play around with mathematics on paper and in your mind, helping you to get a concrete feel for a subject that many people view as painfully abstract.

The prose is clear and well-written: there is just the right amount of discussion to elucidate necessary points, while allowing the book to remain fairly compact. Exercises are fun but difficult and many require genuine creativity.

I also really like the choice of topics: although this book is introductory (with respect to abstract algebra, it presupposes some knowledge of linear algebra), because it focuses only on groups (as opposed to also trying to handle rings & fields) it is able to get into some more advanced and very interesting topics and applications in later chapters. This book will give you a lot more than can be covered in a single semester undergrad course, and while it doesn't exactly make the best reference text, it will be a book you will want to keep coming back to, if only to study some of the more advanced material.

There are differing perspectives on the teaching of abstract algebra: some people like to start with group theory exclusively in a first course, and treat rings, fields, and other structures in later courses. Other people recommend more integrated approaches, or approaches starting from rings. While I can't say that either approach is better, I can say that this book takes the first approach, focusing exclusively on groups and assuming little prior background..and for a first course in abstract algebra, this book is an excellent choice.

Excellent introduction to group theory.......2004-11-02

Please note that the other reviews here are obviously for some other book. This is not an advanced text on bifurcations and stability. It is an introductory book on group theory. I have been using this book for self study. It is well suited to this purpose. The book uses symmetry to unify and motivate the study of groups. The discussion of the symmetry groups of Platonic solids is both enjoyable in itself and useful for visualizing groups. The chapters are very short. The exercises are well suited to gaining insight into the material.

interesting format.......2000-04-01

The book consists solely of exercises and hints for every exercise, which he curiously calls "answers". This book is perfect if you are looking to review geometrically-tinged algebraic structures like matrix groups, symmetry groups, and wallpaper groups. There is also some basic pure algebra in here. I don't think this book would work all that well for a student new to algebra, although someone with some backgroud in algebra can definitely get something out of the geometric chapters.

Average customer rating:

clear, concise book
A Group Theory book that allows students to learn
A much needed breath of fresh air!

Molecular Symmetry and Group Theory
Robert L. Carter
Manufacturer: Wiley
ProductGroup: Book
Binding: Paperback

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ASIN: 0471149551

Book Description

A Thorough But Understandable Introduction To Molecular Symmetry And Group Theory As Applied To Chemical Problems! In a friendly, easy-to-understand style, this new book invites the reader to discover by example the power of symmetry arguments for understanding theoretical problems in chemistry. The author shows the evolution of ideas and demonstrates the centrality of symmetry and group theory to a complete understanding of the theory of structure and bonding. Plus, the book offers explicit demonstrations of the most effective techniques for applying group theory to chemical problems, including the tabular method of reducing representations and the use of group-subgroup relationships for dealing with infinite-order groups. Also Available From Wiley:
* Concepts and Models of Inorganic Chemistry, 3/E, by Bodie E. Douglas, Darl H. McDaniel, and John J. Alexander 0-471-62978-2
* Basic Inorganic Chemistry, 3/E, by F. Albert Cotton, Paul Gaus, and Geoffrey Wilkinson 0-471-50532-3

Customer Reviews:

clear, concise book.......2003-10-09

this small book on symmetry and group theory is easy to understand and packed with examples. it is a small book (only about 300 pages) but everything in it is relevant and to the point. the writing is easy to grasp and the back includes character tables for all the common symmetry groups. buy it!

A Group Theory book that allows students to learn.......2000-10-27

The strength of this book is its many examples. Carter takes the concepts and applies them to simple inorganic or organic compounds. Very helpful to students. The end of chapter problems are nice as well. A great text and one that I would recommend to students as well as faculty.

A much needed breath of fresh air!.......1998-07-29

This is a text set apart from the pack. It clearly states what other books attempt to describe. There need to be more texts on the market like this. Dr. Carter has taken a subject that has historically been elusive, and presented it in a comprehensive, READABLE volume. This text is helping me through my thesis in chemistry. It is highly practical, easily read, and heavily referenced, all of the qualities, I believe, that make up an excellent text! Excellent work!

Average customer rating:

Top ten classical but nowadays incomplete review of group theory in Physics
I-spin, U-spin, V all spin for I-spin

Lie Groups for Pedestrians
Harry J. Lipkin
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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Symmetry: An Introduction to Group Theory and Its Applications
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ASIN: 0486421856

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.

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