# Calculating a particular amplitude with Feynman diagrams

• I
• Ringo Hendrix
In summary, you can use LaTeX to type out the equations for calculating the first and second order expansions seen in the third image.
Ringo Hendrix
TL;DR Summary
This isn’t homework, I’m self taught. Pardon me for using pictures instead of typing out equations, I have no clue how to do that. So please don’t downvote this for that :-) I’m just really desperate to learn this.
So I’m trying to compute the probability amplitude of an electron with momentum p1 and a positron with momentum p2 annihilating into a photons with momenta q1 and q2.

My question is how do you use Feynman diagrams to calculate the first and second order expansions (seen in the third image)? I wouldn’t mind a step-by-step with minimal assumption similar to the pictures I posted. Any help would be greatly appreciated. Again I’m sorry about the pictures, but I really am unsure how to type out the equations but I hope and assume my writing is legible enough.

What I have so far

#### Attachments

• 7B979D15-FFE5-4414-B78A-CC9B5C69FACC.jpeg
47.2 KB · Views: 246
Ringo Hendrix said:
I really am unsure how to type out the equations

You do it using LaTeX:

https://www.physicsforums.com/help/latexhelp/
Please take the time to learn it and use it to type your equations. The issue is not just legibility but being able to quote parts of your post in responses; we can't do that if all the equations are in images. That makes it much harder for people to help you.

Ringo Hendrix
Ringo Hendrix said:
This isn’t homework, I’m self taught. [...] I’m just really desperate to learn this.
But,... presumably you are learning from QFT textbook(s), yes? If so, which one(s)? If not, go get a copy of (e.g.,) Peskin & Schroeder.

My question is how do you use Feynman diagrams to calculate the first and second order expansions (seen in the third image)? [...] I wouldn’t mind a step-by-step with minimal assumption [...]
Any respectable QFT textbook should do that. Best to try and learn from the textbook first, then come back here to clarify any details or steps that you don't follow, or can't figure out (but if you do this, be sure to cite page+eqn numbers in the book).

## 1. How do I determine the amplitude for a specific Feynman diagram?

To calculate the amplitude for a Feynman diagram, you will need to use the Feynman rules, which involve assigning mathematical expressions to each component of the diagram, such as propagators and vertices. By following these rules and performing the necessary calculations, you can determine the amplitude for your specific diagram.

## 2. What is the significance of Feynman diagrams in particle physics?

Feynman diagrams are a visual representation of the mathematical calculations involved in particle interactions. They allow scientists to easily visualize and analyze complex interactions between particles, making it a valuable tool in understanding the fundamental laws of nature.

## 3. Can I use Feynman diagrams to calculate amplitudes for all types of particle interactions?

Yes, Feynman diagrams can be used to calculate amplitudes for all types of particle interactions, including electromagnetic, strong nuclear, and weak nuclear interactions. However, the specific Feynman rules and calculations may vary depending on the type of interaction.

## 4. How do I know if my calculated amplitude is accurate?

To determine the accuracy of your calculated amplitude, you can compare it to experimental data. If the calculated amplitude matches the experimental results, then it is considered accurate. Additionally, you can also perform mathematical checks and use other theoretical models to validate your calculations.

## 5. Are there any limitations to using Feynman diagrams to calculate amplitudes?

While Feynman diagrams are a powerful tool in particle physics, they do have some limitations. They may become increasingly complex for higher-order interactions, and they do not take into account the effects of quantum field theory. Additionally, Feynman diagrams may not accurately represent all aspects of a particle interaction, such as spin and polarization.

• High Energy, Nuclear, Particle Physics
Replies
2
Views
1K
• Quantum Physics
Replies
134
Views
8K
• Quantum Physics
Replies
6
Views
1K
• Quantum Physics
Replies
4
Views
2K
• Quantum Physics
Replies
7
Views
1K
• MATLAB, Maple, Mathematica, LaTeX
Replies
3
Views
2K
• Quantum Physics
Replies
4
Views
2K
• Quantum Physics
Replies
15
Views
2K
• Quantum Physics
Replies
2
Views
904