vanhees71 said:A very good book about all the group-theoretical aspects is
R. U. Sexl, H. K. Urbantke, Relativity, Groups, Particles,
Springer, Wien (2001).
(A , B) \otimes (A^{\prime} , B^{\prime}) = (A + A^{\prime} , B + B^{\prime}) \oplus (A + A^{\prime} - 1 , B + B^{\prime}) \oplus \cdots \oplus (|A - A^{\prime}| , B + B^{\prime}) \oplus (A + A^{\prime} , B + B^{\prime} - 1) \oplus \cdots \oplus (|A - A^{\prime}| , |B - B^{\prime}|) .MichaelJ12 said:How did you go from the third line to the fourth line?
Almost all books on group representations in general and the representation theory of the Lorentz group \mbox{SL}(2 , \mathbb{C}) in particular teach you these stuff. The latter can be found in all textbooks on Supersymmetry.Could you recommend a good book?
samalkhaiat said:(A , B) \otimes (A^{\prime} , B^{\prime}) = (A + A^{\prime} , B + B^{\prime}) \oplus (A + A^{\prime} - 1 , B + B^{\prime}) \oplus \cdots \oplus (|A - A^{\prime}| , B + B^{\prime}) \oplus (A + A^{\prime} , B + B^{\prime} - 1) \oplus \cdots \oplus (|A - A^{\prime}| , |B - B^{\prime}|) .
Almost all books on group representations in general and the representation theory of the Lorentz group \mbox{SL}(2 , \mathbb{C}) in particular teach you these stuff. The latter can be found in all textbooks on Supersymmetry.
I have already said that you can learn about this stuff from all textbooks on supersymmetry. I just know this stuff because it is my business to know it.MichaelJ12 said:I meant where did you learn the physical meaning and significance of the gamma matrices projecting out certain spins.
Then all textbooks by Weinberg are right for you :-)).MichaelJ12 said:Thank you very much. I love those kinds of books. Have you read other books that belong to the same category as Relativity, Groups, Particles, meaning that they are meant to impart understanding? I only want books about "advanced" physics or mathematics like quantum field theory, general relativity, differential geometry, topology, and any other branches of pure mathematics.