# Group Theory Basics for Physics Students

• dEdt
In summary, the conversation is about a student looking for a brief introduction to group theory in order to understand terms used by their professor when discussing spin and isospin. The recommended books for this purpose are Georgi's "Lie Algebras in Particle Physics," Hammermesh's "Group Theory and its Application to Physical Problems," and Barnes' "Group theory for the Standard Model of Particle Physics and Beyond." The conversation also mentions that Lie groups like SU(3) are not considered basic by mathematicians and suggests the book "Group Theory and Chemistry" by David Bishop as a more approachable option.

#### dEdt

My prof has been throwing around some group theory terms when talking about spin and isospin (product representations, irreducible representations, SU(3), etc.) I'm looking for a brief intro to group theory, the kind you might find in a first chapter of a physics textbook, so I can get familiar with what he's talking about. Thanks.

This is actually a very common thing for physics students to want, and it's also a very common thing for them to complain about when they realize Lie groups are not a subject that can be learned from one chapter. Many physics departments offer a semester-long course on the kinds of Lie groups you see in physics.

The best book I can recommend is Georgi's "Lie Algebras in Particle Physics." If you read the first few chapters you should understand all the topics you mentioned. Other possible books are Hammermesh's "Group Theory and its Application to Physical Problems" or Barnes' "Group theory for the Standard Model of Particle Physics and Beyond." All these books give a physicist's version of group theory without all the fussiness you'd find in a math book on Lie groups.

Anyway, Lie groups like SU(3) would not be considered "very basic group theory" by mathematicians. If you take a math department's undergrad semester-long group theory intro course, most professors won't even make it to to continuous groups! An example of a math book that covers this kind of "very basic" group theory would be Fraleigh's "A First Course in Abstract Algbebra".

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Here is one that should be nicer to learn from than a pure math book:

Group Theory and Chemistry - David Bishop

Finite groups only but it looks comprehensive.