Peskin & Schroeder QFT 5.6 Need help

In summary, the individual is seeking help with problem 5.6 (b) in Peskin + Schroeder QFT. They are struggling with getting rid of a term involving three gamma matrices in their amplitude. They have two terms of the form and are wondering how to evaluate the first term using the Fierz identity from 5.3. They provide an equation and ask for help with applying the Fierz identity. They also mention trying to solve 5.3 by adding 1 and then applying the Fierz identity, but are unsure how to handle the term consisting of 3 matrices in 5.6.
  • #1
philipke
5
0
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
 
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  • #2
Sorry here again the equation:

[tex]\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) [/tex]

+ the same term with [tex] k_1 <-> k_2 [/tex] and [tex] \mu <-> \nu [/tex]

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

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

and then apply the Fierz identity. The problem is that in 5.6 I get this term consisting of 3 matrices.
 
Last edited:
  • #3
Well if I calculate a bit I get finally something like

[tex]
k_1\!\!\!/u_R(p_1)\bar{u}_R(k_1)
[/tex]

and further terms of that type. What can i do with that?
 
  • #4
Please remove the thread!
 

Related to Peskin & Schroeder QFT 5.6 Need help

1. What is the main concept behind Peskin & Schroeder QFT 5.6?

The main concept behind Peskin & Schroeder QFT 5.6 is the study of quantum field theory (QFT) and its application to particle physics. It covers topics such as Feynman diagrams, renormalization, and scattering processes.

2. Why is help needed for Peskin & Schroeder QFT 5.6?

Help may be needed for Peskin & Schroeder QFT 5.6 because it is a complex subject that requires a strong understanding of mathematics and theoretical physics. It can be challenging to grasp the concepts and solve the problems without proper guidance.

3. What are some common difficulties in understanding Peskin & Schroeder QFT 5.6?

Some common difficulties in understanding Peskin & Schroeder QFT 5.6 include comprehending the mathematical notation, understanding the physical implications of the equations, and applying the concepts to real-world scenarios. It may also be challenging to visualize abstract concepts, such as virtual particles and gauge theories.

4. What are some useful resources for understanding Peskin & Schroeder QFT 5.6?

Some useful resources for understanding Peskin & Schroeder QFT 5.6 include textbooks on quantum field theory, online lectures and tutorials, and practice problems with solutions. It may also be helpful to consult with a professor or join a study group to discuss concepts and problem-solving techniques.

5. How can one improve their understanding of Peskin & Schroeder QFT 5.6?

To improve understanding of Peskin & Schroeder QFT 5.6, it is important to have a strong foundation in mathematical methods and quantum mechanics. Additionally, practicing problem-solving and seeking guidance from experts can help in understanding the concepts and their applications. It may also be helpful to review and reinforce concepts from previous chapters before moving on to more complex topics.

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