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Frontiers in Physics
Lie Algebras in Particle Physics: From Isospin to Unified Theories
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.
340 pages, Paperback
First published January 1, 1982
11 people are currently reading
123 people want to read
About the author
Howard Georgi
6 books5 followersHoward Mason Georgi III is Harvard College Professor and Mallinckrodt Professor of Physics at Harvard University, where he is also Director of Undergraduate Studies in Physics and Master of Leverett House. In 1995 he was elected to the National Academy of Sciences and received the J.J.Sakurai Prize. In 2000 he shared the Dirac Medal with Jogesh Pati and Helen Quinn.
He is best known for early work in Grand Unification and gauge coupling unification withing SU(5) (Georgi-Glashow model) and SO(10) groups.
He later proposed the supersymmetric Standard Model with Savas Dimopoulos in 1981.
It is also worth mentioning his role in the Georgi-Quinn-Weinberg computation showing that the natural mass scale of unification is relatively close to the Plank scale and that the proton lifetime can naturally be extremely long.
He has since worked on several different areas of physics including composite Higgs models, heavy quark effective theory, dimensional deconstruction and little Higgs theories.
Most recently, with Arkani-Hamed and Cohen, he has found a class of 4-dimensional field theories in which extra dimensions can arise dynamically, providing a new slant of the meaning of space. The topological properties of such theories may shed light on critical issues such as the breaking of SU(2)xU(1) and supersymmetry. He continues to study these issues in the hopes they will shed light on the meaning of gauge symmetry.
He is best known for early work in Grand Unification and gauge coupling unification withing SU(5) (Georgi-Glashow model) and SO(10) groups.
He later proposed the supersymmetric Standard Model with Savas Dimopoulos in 1981.
It is also worth mentioning his role in the Georgi-Quinn-Weinberg computation showing that the natural mass scale of unification is relatively close to the Plank scale and that the proton lifetime can naturally be extremely long.
He has since worked on several different areas of physics including composite Higgs models, heavy quark effective theory, dimensional deconstruction and little Higgs theories.
Most recently, with Arkani-Hamed and Cohen, he has found a class of 4-dimensional field theories in which extra dimensions can arise dynamically, providing a new slant of the meaning of space. The topological properties of such theories may shed light on critical issues such as the breaking of SU(2)xU(1) and supersymmetry. He continues to study these issues in the hopes they will shed light on the meaning of gauge symmetry.
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Displaying 1 - 9 of 9 reviews
July 20, 2020
This is a very good book introduction group theory, Lie algebras and representations for physicists. The explanations are clear throughout, full of example and anecdotes. It takes its time to get to some of the central results but that is only to make sure you have really understood the previous topic before moving on to the next. This is by far the best explanation of roots and the Cartan classification that I have encountered. It was very intuitive and very easy to follow.
It is very much aimed at physicists, it uses notation and intuition straight from quantum mechanics, which a pure mathematician might find confusing. Further, it is not a completely rigorous and thorough discussion of the topic which some people might dislike. For example, it does not assume familiarity with differential geometry (like a physicist would get in a general relativity course) so some of the more geometrical aspects of Lie groups and algebras are skipped over. And also, there is little care in the distinction between real and complex Lie algebras so the discussion of spinors sweeps many details under the rug (e.g. covering groups and projective representations).
However, the intuition gained in the way this is explained in this book definitely goes a long way and it would be very useful for the reader who is interested in the more sophisticated approaches. And at least coming from a physicist perspective, the constant call-backs to quantum mechanics really do help a lot with the intuition.
There were a few chapters on symmetry breaking and grand unified theories that are a bit outdated given the developments in particle physics since the time of writing. The perspective held in this book is no longer the standard practice. However, it is not wholly inappropriate, and the discussions are still interesting in their own right.
As a final remark I should point out that some topics that might be interesting for physicists are omitted, namely, Casimir elements and induced representations (that is, representations of the Poincaré group).
It is very much aimed at physicists, it uses notation and intuition straight from quantum mechanics, which a pure mathematician might find confusing. Further, it is not a completely rigorous and thorough discussion of the topic which some people might dislike. For example, it does not assume familiarity with differential geometry (like a physicist would get in a general relativity course) so some of the more geometrical aspects of Lie groups and algebras are skipped over. And also, there is little care in the distinction between real and complex Lie algebras so the discussion of spinors sweeps many details under the rug (e.g. covering groups and projective representations).
However, the intuition gained in the way this is explained in this book definitely goes a long way and it would be very useful for the reader who is interested in the more sophisticated approaches. And at least coming from a physicist perspective, the constant call-backs to quantum mechanics really do help a lot with the intuition.
There were a few chapters on symmetry breaking and grand unified theories that are a bit outdated given the developments in particle physics since the time of writing. The perspective held in this book is no longer the standard practice. However, it is not wholly inappropriate, and the discussions are still interesting in their own right.
As a final remark I should point out that some topics that might be interesting for physicists are omitted, namely, Casimir elements and induced representations (that is, representations of the Poincaré group).
May 2, 2016
I learned SU(3) from this book, and for that I'm grateful. While standard texts on quantum field theory and particle physics mostly adequately cover the more pedestrian groups like SU(2), SO(3), etc, SU(3) is too complicated to be done justice by only the topical, passing mention given in these books. Georgi covers roots, weights, and the "anatomy" of Lie groups, with SU(3) occupying a starring role throughout the work. The text, however, is terse and formal (it is based on lecture notes). Though the breadth of topics is impressive (Lie algebra basics to GUTs to spinor representations), many are given short shrift and so this book is hit or miss in some places. But for SU(3) it is good. Read it for SU(3).
April 7, 2021
Perfect introduction to such a beautfiul topic in physics, loved the explanation on weights/simple roots (with a lot of examples). Its definetely aimed at physicists and one can probably learn most of the group theory ideas used in physics. I'd still recommend to read an additional book to this one, that delves more in the mathematical structure of things, like Representation Theory from Fulton and Harris.
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September 17, 2023This book looked interesting and accessible in the first ~50 pages, but, for someone who is not a practicing particle physicist, the explanations could have been better. I was excited to get this book, but it was hard to stomach the author's explanations (I'm not looking for rigor) of why certain things are true so I decided to stop and return the book. I was at the doorstep of reading about root vectors.
September 24, 2020
Clear, concise, and easy to follow.
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October 22, 2023Dado un grupo G, una aplicación de los elementos del grupo a un conjunto de operadores lineales se denomina una representación del grupo.
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October 22, 2023Dado un grupo G, una aplicación de los elementos del grupo a un conjunto de operadores lineales se denomina una representación del grupo.
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February 8, 2017hard to follow
April 20, 2015
If you're a particle physicist, read it. Period.
Displaying 1 - 9 of 9 reviews