Understanding Renormalisation Calculations in Field Theory

[latentcorpse]

On p 51 of these notes:
http://www.damtp.cam.ac.uk/user/ho/Notes.pdf ,

I'm trying to follow the calculation $\int \frac{d^dk}{(2 \pi )^d} \frac{1}{(k^2+m^2)^2}= - \frac{\partial}{\partial m^2} \dots$

It looks to me like we can just use the calculation above and then take the derivative at the end but somehow this isn't working as whilst he has lowered the power on the m^2, he hasn't multiplied through by the old power. Additionally, the argument of the Gamma function has changed!

What's going on?

 

[fzero]

Have you tried computing the ratio of your result to his?

 

[latentcorpse]

Have you tried computing the ratio of your result to his?

You mean that if I expand out the gamma function in both expressions, I should find they are the same?

Even so though, how did he end up with his version rather than mine?

 

[fzero]

He just used an identity to tidy up the result a bit.

 

[latentcorpse]

He just used an identity to tidy up the result a bit.

So he does it my way then uses $\Gamma(\alpha+1)= \alpha \Gamma(\alpha)$?