Peskin & Schroeder QFT 5.6 Need help

[philipke]

Hey!

I need some help for problem 5.6 (b) in Peskin + Schroeder QFT. I can't get rid of the term including three gamma matrices in my amplitude.

I get two terms of the form:

\frac{-\gamma^{\nu}*\slash{k_2}*\gamma^{\mu} + 2\gamma^{\nu}p_1^{\mu}}{-2*p_1*k_2}

and the same with k_1 <-> k_2 and \nu <-> \mu.

How can I evaluate the first term in the numerator using the Fierz identiy from 5.3?

Thanks in advance!

Philip

 

[philipke]

Sorry here again the equation:

$$\bar{u_R}(p_2)\frac{-\gamma^{\nu}k_2\!\!\!/\gamma^{\mu} + 2\gamma^{\nu}p_1^{\mu}}{-2p_1k_2}u_R(p_1)$$

+ the same term with $$k_1 <-> k_2$$ and $$\mu <-> \nu$$

This is one factor in my amplitude (from the propagator). How can I apply the Fierz identity?

I could solve 5.3 adding $$1 = \frac{1}{4}[\gamma_{\mu}]_{ab}[\gamma^{\mu}]_{ba}$$

and then apply the Fierz identity. The problem is that in 5.6 I get this term consisting of 3 matrices.

 

[philipke]

Well if I calculate a bit I get finally something like

$$k_1\!\!\!/u_R(p_1)\bar{u}_R(k_1)$$

and further terms of that type. What can i do with that?

 

[philipke]

Please remove the thread!