Book recommendation for representation theory(physicist)

  • #1

Could anyone recommend me a good book that will teach me the kind of group/representation theory I would need to understand these things when applied to QFT (Lie Algebra, Lorentz group, SU(2) etc)?

  • #2
Cornwell's books on group theory are good (but a bit long maybe...)
Georgi's is a reference.
  • #3
Lie Algebras in Particle Physics, second edition is not one of the best books but the best book of all!
  • #4
I would recommend two books:

Lie Algebra in Particle Physics, from Howard Georgi
Quantum Mechanics- Symmetries, from Walter Greiner.

These two books complement each other in the sense that Georgi spans a wide range of techniques, but is not always rigorous and mainly focuses on calculational techniques and how those techniques are implemented in advanced particle physics, from particle classification to symmetry breaking and Unification theories. The aim is NOT to explain Unification or symmetry breaking but really to explain what is the role of group theory in these topics.

Greiner's book is much more thorough, as everything is rigorously proved mathematically, starting from early concept of symmetries to thoroug developpment of SU(2) and SU(3). At first it might seems insane to spend so much time to explain in crazy details the mathematical details of SU(2), while it is, in itself a so simple group. The answer lies in the root system and character theory, where the fundamental tool is pretty much identifying all the SU(2) multiplets existing in a given group. Georgy explains this fairly well when calculating the roots of a group.

To summarize, Greiner's book is better explain, but because of this, it covers less (it stops more or less with charachter theory and Dynkin diagram/Cartan approach included). Georgi has less explanations, is more computational (a kind of "recipe book") so it goes further in terms of content. You would still need a theory book to understand the foundation of these calculation however, which is why i studied Greiner's along with Georgi.

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