How to calculate Feynman amplitude in Fish diagram

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Alpha2021
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I am familiar with the process of calculating cross sections using tree-level Feynman diagrams. Currently, I'm keen on learning how to calculate the Feynman amplitude for a specific diagram displayed in the attached images. I'm wondering if there are any study materials available that offer a step-by-step approach to comprehending and calculating this particular process. Specifically, I'm interested in cases where x_3 and x_4 can be either scalar, fermion, or gauge boson particles.
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Any QFT book, like Srednicki or Peskin & Schroeder
 
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1. What is a Feynman amplitude in Fish diagram?

A Feynman amplitude in Fish diagram is a mathematical expression that represents the probability amplitude for a particle to move from one point to another in a Feynman diagram. It takes into account all possible paths that the particle can take and is an important tool in calculating interactions between particles in quantum field theory.

2. How do you calculate a Feynman amplitude in Fish diagram?

To calculate a Feynman amplitude in Fish diagram, you need to first construct the diagram by drawing the relevant particles and their interactions. Then, you need to assign mathematical expressions to each line and vertex in the diagram. Finally, you use Feynman rules and mathematical techniques to simplify the diagram and calculate the amplitude.

3. What are the Feynman rules for calculating a Fish diagram?

The Feynman rules for calculating a Fish diagram involve assigning mathematical expressions to each line and vertex in the diagram. The rules state that each line represents a propagator, which is a mathematical expression that describes the probability of a particle moving from one point to another. Each vertex represents an interaction between particles, and the mathematical expression for the vertex depends on the type of interaction.

4. What are the mathematical techniques used to simplify a Feynman amplitude in Fish diagram?

There are several mathematical techniques that can be used to simplify a Feynman amplitude in Fish diagram. These include using Feynman rules to replace lines and vertices with their corresponding mathematical expressions, using mathematical identities to simplify the expressions, and performing integrals to eliminate variables.

5. Can Feynman amplitudes in Fish diagrams be used to make predictions about particle interactions?

Yes, Feynman amplitudes in Fish diagrams are an important tool in making predictions about particle interactions. By calculating the amplitude for a specific interaction, scientists can determine the probability of that interaction occurring and make predictions about the behavior of particles in different scenarios. These predictions have been tested and confirmed through experiments, making Feynman amplitudes in Fish diagrams an essential part of particle physics research.

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