Derivating a Yukawa theory loop-integral !


by Ace10
Tags: derivating, loop integral, loopintegral, quantum field theory, renormalization, theory, yukawa
Ace10
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#1
Jan20-14, 05:30 AM
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Hello fellow physicists,

during some calculations for a project regarding Renormalization, I had a difficulty in computing a derivative of a loop integral in Yukawa theory. The thing i'm reffering to can be found in Peskin and Schroeder's book, Introduction to QFT , in Chapter 10 page 329-330.

Question #1:

How the gamma function's argument changes from "1-d/2" (10.33) to "2-d/2" (10.35) ?

Question #2:

Could please somebody show me a detailed calculation of the derivation? I cannot get the finel form, with "x(1-x)" in the numerator and plus the denominator has power "2-d/2" and i think that normally the power should be "-d/2"


Thank you very much in advance..
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Bill_K
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#2
Jan20-14, 06:43 AM
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Quote Quote by Ace10 View Post
How the gamma function's argument changes from "1-d/2" (10.33) to "2-d/2" (10.35) ?
When you take the derivative of the denominator, a factor of 1-d/2 comes out, and then use the identity zΓ(z) = Γ(z+1).


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