An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems.
Wu-Ki Tung, born in Kunming, China (1939), died on Mar 30, 2009 in Seattle, Washington. He was educated at National Taiwan University andreceived his Ph.D. at Yale University in 1966. Wu-Ki Tung was Professor Emeritus at Michigan State University (MSU), and Affiliated Professor at University ofWashington. He was a theoretical physicist, whose main interestwas the study of phenomenological aspects of high energy particle physics,particularly in the field of Quantum Chromodynamics (QCD) and, more specifically, of parton distributions in hadrons.Parton distribution functions areamong the standard inputs needed to compare theoretical calculations to experimentslike Fermilab Tevatron and the CERN Large Hadron Collider (LHC).Wu-Ki Tung was the founder of The Coordinated Theoretical-Experimental Project on Quantum Chromodynamics Collaboration(CTEQ).He led the CTEQ global QCD analysis group to determine parton distributionfunctions from high energy scattering experiments of different types.Wu-Ki Tung'sgroup at MSU recognized the importance of developing a systematic error analysis for the global analysis, which hasnow been widely used in various experimental and theoretical analyses. Wu-Ki Tung was a founding member of Overseas Chinese Physics Association (OCPA)and had been actively involved in its development and activities ever since.He was also the author of an influential book Group Theory in Physics, which is used all over the world.
Group Theory In Physics Wu-ki Tung Pdf 79
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I am looking for a good source on group theory aimed at physicists. I'd prefer one with a good general introduction to group theory, not just focusing on Lie groups or crystal groups but one that covers "all" the basics, and then, in addition, talks about the specific subjects of group theory relevant to physicists, i.e. also some stuff on representations etc.
Here and there there are some insights or unexpected facts (mostly in the introductions and appendices of each chapter), but the rest are verbose and can be reduced, especially when math is involved, so you may want to have good foundation before skipping them. The author explicitly states that he tends to "favor those are not covered in most standard books, such as the group theory behind the expanding universe", and his choices reflect his own likes or dislikes. So if you want to have a standard knowledge in standard book, this is not your choice. The contract of the author with Princeton requires the title to have the bit "in the nutshell", which I think misleading.
While the physical meanings of mathematical objects are emphasized, mathematical meanings of mathematical objects are underconsidered. Trace is only a sidenote thing, not the character of equivalent irreducible representations. Schur's lemma is mentioned only in one sentence. The whole representation theory is discussed very fleeting (only one subsection in the Lie group theory section), before going straight to important groups: $SU(2)$, Lorentz group, Poincar group.
"This book is an excellent introduction to the use of group theory in physics, especially in crystallography, special relativity and particle physics. Perhaps most importantly, Sternberg includes a highly accessible introduction to representation theory near the beginning of the book. All together, this book is an excellent place to get started in learning to use groups and representations in physics."
There is a new book called Physics From Symmetry which is written specifically for physicists and includes a long, very illustrative introduction to group theory. I especially liked that here concepts like representation or Lie algebra aren't only defined, but motivated and explained in terms that physicists understand. Plus no concepts are introduced which aren't needed for physics, which was always a big problem for me when I read books for mathematicians. Group theory is a very big subject and mathematicians find a lot of things interesting that aren't very relevant for physicists.
I would recommend A. O. Barut and R. Raczka "Theory of Group Representations and applications". It is about Lie algebras and Lie groups, and you are asking for general group theory, but this book, in my opinion, would be useful to a physicists. The applications are to physics, mainly quantum theory.
Edit: Forgot to comment on the last part of the questions. I think Wigner is a good read. You'll not learn much about general group theory, but you will learn about representation theory of the Poincare group and some general techniques from representation theory like the Mackey machine for induced representations.
Well, in my dictionary "group theory for physicists" reads as "representation theory for physicists" and in that regard Fulton and Harris is as good as they come. You'll learn all the group theory you need (which is just a tiny fragment of all group theory) along the way.
Classical Groups for Physicists , by Brian G. Wybourne (1974) Wiley.Has the most usable Lie Group theory beyond monkey-see-monkey do SU(2) and SU(3). Is addressed to readers who habitually illustrate and attempt understand abstract mathematical notation (a rare species). Once one learns how to use it, one may spend a lifetime doing just that. Dynamical group treatment for solvable systems a veritable classic.
I took a course on group theory in physics (based on Cornwell) and even though I followed all of the proofs, I had no idea how it might help me solve physical problems until I picked up Tinkham's Group Theory and Quantum Mechanics. Literally just reading 5 pages (the introduction) made a tremendous impact on my understanding of why group theory is important to physical applications and what sort of group/representation properties I should be looking for. After almost every major group/representation result, he shows how it relates to a quantum calculation. His approach and examples might be considered dated (not much on Lie groups and a lot on crystallography) but if you're just getting acquainted with the field, I think it's the best around.
Sternberg's book is excellent and illuminating but perhaps a bit hard for a beginner. I recommend as a first reading Lie Groups, Lie Algebras, and Representations. The book deals with representation theory of Lie groups of matrices. After reading this I also recommend the Sternberg's book for physical applications and the topological point of view of group theory.
I am surprised no one has mentioned Lipkin yet. His "Lie Groups for Pedestrians" uses notation that is not too out of date, since it was written in the early 60s. He covers the use of group theory in nuclear physics, elementary particle physics, and in symmetry-breaking theories. From there, it is only a small jump to more modern theories.
Heine's "Group Theory in Quantum Mechanics" and Weyl's "The Theory of Groups and Quantum Mechanics" are also classics, but their notation really is old. And both books are too old to cover use of group theory with QCD or symmetry breaking. But both these books explain the philosophy of the use of groups in QM, which later authors seem to usually assume you already know. Heine also includes a lot more than most about the application of finite and 'point' crystallographic groups. But he does still seem to take a more mathematically abstrat approach than most physicists need: as Lipkin points out, the interests of a physicist and those of a mathematician in group theory really are different: as an example of the difference, Lipkin even mentions the rank of Lie algebras without ever defining it:(
There is a recent textbook which gives a fairly complete and concise presentation of group theory, covering both structure and representations of both finite and continuous (Lie) groups, with a brief discussion on applications to music (finite groups) and elementary particles (Lie groups). The target level is advanced undergraduate and beginning graduate. It is freely available at
Instead of following the books, I've been teaching group theory for physicists by following these papers below. The idea is to study the papers from top to bottom, and use a traditional books (e.g. Tinkham, Hammermesh, Dresselhaus, Joshi) to fill the gaps.
Group theory for physicists is a branch of mathematics that deals with the study of symmetries in physical systems. It is used to describe the behavior of particles and fields in physics, and to understand the fundamental laws of nature.
Group theory is important in physics because it provides a powerful framework for understanding and predicting the behavior of physical systems. It allows physicists to identify and classify symmetries in nature, and to use these symmetries to make predictions about the behavior of particles and fields.
Group theory is used in physics to analyze the symmetries of physical systems and to classify them into different groups. These groups can then be used to identify the properties and behaviors of particles and fields, and to make predictions about their interactions.
Group theory has many applications in physics, including in quantum mechanics, particle physics, and cosmology. It is used to explain the properties and interactions of subatomic particles, the symmetries of the laws of physics, and the structure of the universe.
Group theory can be challenging to understand for physicists, as it involves abstract mathematical concepts and techniques. However, with proper training and practice, it can be a powerful tool for solving complex problems in physics and understanding the fundamental laws of nature.
My question about group theory and if you have a book you could recommend for some foundation: specifically chemical applications of group theory with emphases on 3-center bonding, symmetry-based selection rules for cyclization, and 3D lattices and their symmetries. be457b7860
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