# What am I missing here? (QFT: ##e^- - p## scattering)

• B
• Wrichik Basu
In summary, the conversation discusses the author's explanation of the Feynman diagram for electron-proton scattering and the corresponding Feynman amplitude. The author also mentions the use of bold and normal font to represent 3-vectors and 4-vectors respectively. The conversation ends with the question of how to write terms for ##l^{\mu\nu}## and ##h_{\mu\nu}## based on ##\mathcal{M}## and the suggestion to review identities for traces and contractions with gamma matrices and polarization spinors.
Wrichik Basu
Gold Member
I am currently reading Particle Physics by Palash Pal. In one place, the author shows the Feynman diagram for the electron-proton scattering:

Then, he writes the Feynman amplitude for the process: $$i \mathcal{M} \ = \ \left[ \bar{u}(\vec{k'}) i e \gamma^\mu u(\vec{k}) \right] \frac{-ig_{\mu\nu}}{q^2} \left[\bar{u}(\vec{p'}) i e \Gamma^\nu u(\vec{p}) \right]$$ Then he writes,

where,

and

After this, he proceeds to find the expression for the ##\Gamma## in ##h_{\mu\nu}##.

My question is, how does he write the terms for ##l^{\mu\nu}## and ##h_{\mu\nu}## just by looking at ##\mathcal{M}##? I am sure I am missing something, and the answer is very trivial, but since I have none to ask, I hope you will help me out.

Notation used: According to the author, bold font means a 3-vector, while normal font means a 4-vector. So, k is a 4-vector, while k is the corresponding 3-vector.

Has the book gone through the identities for traces and contractions with the gamma matrices and polarization spinors?

DarMM said:
Has the book gone through the identities for traces and contractions with the gamma matrices and polarization spinors?
Yes, it has, but not in great details. I might be forgetting something. I need to look those up.

Wrichik Basu said:
Yes, it has, but not in great details. I might be forgetting something. I need to look those up.
They're essentially responsible for the result. I'd look them up again and remember what indices are being contracted.

vanhees71 and Wrichik Basu
DarMM said:
They're essentially responsible for the result. I'd look them up again and remember what indices are being contracted.
Seems that I have to take up a different book.

## What is QFT and how does it relate to ##e^- - p## scattering?

QFT stands for quantum field theory, which is a theoretical framework used to describe the behavior of subatomic particles and their interactions. In the context of ##e^- - p## scattering, QFT is used to calculate the probability of an electron and a proton interacting and exchanging energy and momentum.

## Why is ##e^- - p## scattering important in particle physics?

##e^- - p## scattering is important because it allows us to study the fundamental properties of subatomic particles, such as their charge and spin. It also helps us understand the strong and weak nuclear forces that govern interactions between particles.

## What is the significance of the scattering angle in ##e^- - p## scattering?

The scattering angle is the angle at which the electron and proton are deflected after interacting. It provides information about the strength of the interaction and the distance between the particles. By studying the scattering angle, we can gain a deeper understanding of the forces at play.

## How is QFT used to calculate the scattering cross section in ##e^- - p## scattering?

In QFT, the scattering cross section is calculated by considering the probability of the electron and proton interacting at different energies and angles. This is done by using mathematical equations, such as Feynman diagrams, to model the interaction and calculate the probability of it occurring.

## What other factors are important to consider in ##e^- - p## scattering besides the particles' charges?

Besides the charges of the particles, other important factors to consider in ##e^- - p## scattering include the particles' masses, spins, and energies. These properties affect the strength and type of interaction between the particles and can impact the overall outcome of the scattering event.

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