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Question about S(3) spontaneous symmetry breaking in Peskin & Schroeder
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[QUOTE="Antarres, post: 6547101, member: 643619"] Okay well, it is true that rescaling the generators changes this number, since it is a normalization convention. The equation is: $$\text{tr}(t^at^b) = C(r)\delta^{ab}$$ where C(r) is a constant that is dependent on representation, and t's are generators. The representation is taken to be irreducible, and it is said that if we fix this number in one representation, then we fix it in all other representations(although I haven't tried to prove that). That means, from what I get, that this is indeed a convention, however that convention is not giving the same constant for every representation. It is conventional for [B]fundamental representation[/B] of SU(N) to choose: $$\text{tr}(t^at^b) = \frac{1}{2}\delta^{ab}$$ However since he mentioned that in this model we take the scalar field to transform according to the adjoint representation, I figured these generators in (20.35) would also be in adjoint representation. In adjoint representation, for the convention above, we have that: $$\text{tr}(t^at^b) = 3\delta^{ab}$$ That is calculated in Peskin chapter 15.4. It is possible though, that when he rewrote the equation like this, he chose the generators to be in the fundamental representation, it didn't cross my mind he would do that, but I guess it's possible, since this substitution doesn't seem to have anything to do with the transformation of the fields. So maybe you're correct, I just wasn't sure that is the case. [/QUOTE]
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Question about S(3) spontaneous symmetry breaking in Peskin & Schroeder
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