While i'm talking books, is there a Fields, Sets and Algebras for Dummies

In summary, there are three levels of learning for understanding the representation of groups used in physics, such as SU(2) and SU(3). The introductory sections of quantum field theory texts provide a basic understanding of these groups, while specialized texts can help in building representations for these and related groups. A deeper understanding of the mathematical theory of representations is not necessary for most physicists.
  • #1
davelee
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While I'm talking books, is there a "Fields, Sets and Algebras for Dummies"

Where dummies = physicists (me!). I've been baffled thus far by statements such as "SU(2) is a representation of such and such in R^2" and similar statements made in reference to the standard model and isospin. I fail to appreciate the significance probably since I have not ever studied real analysis and fields from a "math" perspective. However, is there a way I could read up on this without being forced to begin with a proof of constructing real numbers from the rational numbers, while still getting the essential properties of fields, etc., and the lingo to go along with it?
 
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  • #2
The representation of SU(2) etc. fall into the area of Lie groups and their Lie algebras. (I have to insist that Lie, a man's name, is pronounced LEE!) There are three levels of learning.

1) Learn the basic groups used in physics (SU(2), SU(3), SO(1,3), and maybe S2(L,C), SU(N), and SO(N). Only specialists need E8. The popular representations are described in the introductory sections of quantum field theory texts, including Ryder and Kaku. Memorize them and you can understand most of what's going on in the standard model.

2) Learn how to build representations yourself for these and closely related groups. You might want to do this if you plan on writing research papers in field or stringy physics. There are specialized texts for this, although the Dover book Group Theory and its Application to Physical Problems by Hammermesch, is a pretty good intorduction, in which you can skip a lot of stuff.

3) Get hung up on the full bore mathematical theory of representations. There are mathematicians right now working on the the represention theory of infinite dimensional things you never heard of and will probably (but not certainly!) never need in physics.
 

1. What is "Fields, Sets and Algebras for Dummies" about?

"Fields, Sets and Algebras for Dummies" is a beginner-friendly book that introduces readers to the fundamental concepts and principles of fields, sets, and algebras in mathematics. It covers topics such as algebraic structures, operations, and equations, and provides clear explanations and examples to help readers understand these concepts.

2. Who is the target audience for this book?

The target audience for this book is anyone who is interested in learning about fields, sets, and algebras but has little to no prior knowledge or experience with these topics. It is also suitable for students who are studying mathematics or related fields and need a refresher on these concepts.

3. What makes "Fields, Sets and Algebras for Dummies" different from other math books?

This book is written in a user-friendly and accessible style, making it easier for readers to understand complex mathematical concepts. It also includes practical examples and exercises to help readers apply what they have learned.

4. Can this book be used as a textbook for a math course?

While "Fields, Sets and Algebras for Dummies" can serve as a supplemental resource for a math course, it is not designed to replace a traditional textbook. It is best used as a self-study guide or reference book.

5. Are there any prerequisites for reading this book?

No, there are no prerequisites for reading "Fields, Sets and Algebras for Dummies". The book starts with the basics and gradually introduces more advanced concepts, making it suitable for readers with little to no prior knowledge of fields, sets, and algebras.

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