# Another question from Srednicki's QFT book.

by MathematicalPhysicist
Tags: book, srednicki
 P: 3,220 Sorry for my questions, (it does seem like QFT triggers quite a lot of questions :-D). Anyway, on page 103 (it has a preview in google books), I am not sure how did he get equation (14.40), obviously it should follow from (14.39), but I don't understand where did -ln(m^2) disappear ? Shouldn't we have an expression like (14.40) but the term (linear in k^2 and m^2) be instead: (linear in k^2,m^2 and ln(m^2)). Cause as far as I can tell from (14.39) $$\Pi(k^2)$$ depends also on ln(m^2), and thus the term "linear in..." should be replaced with "linear also in ln(m^2)", cause as far as I can tell ln(m^2) isn't linear function of m^2, right? Hope someone can enlighten me.
 P: 754 No that's not possibly the case, because even if you have the $- \ln (m^{2})$ it's multiplied with a $D$.. After integration of $D dx$ you will get $(k^{2}+m^{2})ln(m^{2})/6$ so I think the $ln(m^{2})$ is absorbed within the $κ_{A,B}$ But I hope someone can be more helpful
 P: 3,220 In this case we don't have a book preview of pages 166-167 . So I'll write the equations: $$(27.23) ln |\mathcal{T}|^2_{obs} = C_1+2ln \alpha +3\alpha (ln \mu +C_2)+O(\alpha^2)$$ Now he says that "Differentiating wrt ln \mu then gives": $$(27.24)0=\frac{d}{dln \mu} ln |\mathcal{T}|^2_{obs} = \frac{2}{\alpha} \frac{d\alpha}{dln \mu} +3\alpha +O(\alpha^2)$$ Now as far as I can tell when you differentiate: $$\frac{d}{dln \mu} (3\alpha(ln \mu +C_2))=3\alpha + 3 \frac{d\alpha}{dln \mu} (ln \mu +C_2)$$ so where did $$3 \frac{d\alpha}{dln \mu} ln \mu$$ disapper from eq. (27.24)? Don't see why he didn't include this term in eq. (27.24). Anyone?