I have a few questions about the contents in Weinberg, the Quantum Theory of fields Vol1.(adsbygoogle = window.adsbygoogle || []).push({});

First one : At the end of page 77(Sec 2.6), we got -ζ_σ=ζ_σ±1. From this, we could refer that ζ_σ should be proportional to (-1)^σ. But, in the next page, Weinberg concluded that ζ_σ =ζ(-1)^(j-σ). As I said before, -σ in the exponential of (-1) can be easily understood. But, I don't know why ζ_σ should be proportional to (-1)^j.

Second one : It is about the equation below the equation (3.1.21) (page 112, sec 3.2)

The integral variable of this equation is dα, which is Ʃ_(n1,σ1,n2,σ2,....)∫d^3p1 d^3p2 ....

The paragraph below this equation explains how we get '0' in some cases by using the contour integration about E_α. But, in my opinion, dα does not include dE_α. How can we consider the contour integration about E_α ?

Third one : In the last paragraph of page 156(Sec 3.7), Weinberg said we note that k^l Y_lm(k) is a simple polynomial function of the three ........., so in order for M_........ the coefficients M^j_l's'n',lsn must go as k^(l+1/2)k'^(l+1/2) when k and k' go to zero.

I think k^2l Y_lm(k) is also a simple polynomial function, so why did he choose 'l' specially? In addition, I don't understand how we get k^(1/2)k'^(1/2) in k^(l+1/2)k'^(l+1/2) either.

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# Questions in Weinberg The Quantum Theory of Fields Vol 1

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