How to derive a numerator relation in vertex correction in Peskin p191

Thread starter Comanche
Start date Aug 29, 2011
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Correction Derive Peskin Relation Vertex

In summary, a numerator relation in vertex correction is a term in the calculation of Feynman diagrams that involves the vertices and is represented by a numerator function. To derive this relation, the Feynman rules are used to consider all possible combinations of momenta. This is important because it simplifies the calculation process, but there are limitations to its applicability. The derivation of a numerator relation also contributes to our understanding of particle interactions and helps us make predictions and test theoretical models.

Aug 29, 2011

Comanche

i.e.

thank you very much in advance

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Aug 29, 2011

Comanche

i got it, first by l:=k+yq-zp transform k into l, then remove odd terms of l, then use 6.46

1. What is a numerator relation in vertex correction?

A numerator relation in vertex correction refers to a term in the calculation of Feynman diagrams that involves the vertices of the diagram. It is typically represented by a numerator function that contains the momentum variables of the particles involved in the interaction.

2. How is a numerator relation derived in vertex correction?

To derive a numerator relation in vertex correction, the Feynman rules for calculating the amplitude of the diagram are used. The numerator function is obtained by considering all possible combinations of incoming and outgoing momenta and summing over them.

3. What is the importance of deriving a numerator relation in vertex correction?

A numerator relation in vertex correction is important because it allows us to simplify the calculation of Feynman diagrams by reducing the number of terms that need to be evaluated. This can greatly speed up the computation process and make it more manageable.

4. Are there any limitations to deriving a numerator relation in vertex correction?

Yes, there are limitations to deriving a numerator relation in vertex correction. It is only applicable to certain types of Feynman diagrams, specifically those involving interactions between particles. It may not be applicable to diagrams involving external fields or self-interactions.

5. How does the derivation of a numerator relation in vertex correction contribute to our understanding of particle interactions?

The derivation of a numerator relation in vertex correction helps us to understand the underlying structure of particle interactions and how they are related to each other. It also allows us to make predictions about the behavior of particles in certain interactions and helps us to test the validity of theoretical models.