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.
hqbc.jpg
vqvxq.jpg
 
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Any QFT book, like Srednicki or Peskin & Schroeder
 
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FAQ: How to calculate Feynman amplitude in Fish diagram

What is a Feynman amplitude?

A Feynman amplitude is a complex number that represents the probability amplitude for a specific process in quantum field theory. It is calculated using Feynman diagrams, which are pictorial representations of the interactions between particles. The amplitude is essential for determining the likelihood of various outcomes in particle collisions and decays.

How do I identify the components of a Feynman diagram?

In a Feynman diagram, the components include external lines (representing incoming and outgoing particles), internal lines (representing virtual particles), and vertices (where interactions occur). Each component corresponds to specific mathematical factors used in the calculation of the Feynman amplitude.

What rules do I need to follow to calculate the Feynman amplitude?

To calculate the Feynman amplitude, you need to follow several rules, including the Feynman rules for the specific theory you are working with. These rules dictate how to associate mathematical expressions with each element of the diagram, such as propagators for internal lines and interaction vertices for interactions. Additionally, you must integrate over all momenta of the internal lines.

How do I handle loops in Feynman diagrams?

Loops in Feynman diagrams indicate the presence of virtual particles and require the use of loop integrals to calculate the amplitude. You must apply techniques such as regularization and renormalization to handle divergences that may arise from these integrals. The calculation often involves dimensional regularization or cutoff methods to obtain finite results.

What is the significance of the Feynman amplitude in particle physics?

The Feynman amplitude is crucial in particle physics as it provides a way to calculate cross-sections and decay rates for particle interactions. These quantities are experimentally measurable and allow physicists to make predictions about the outcomes of high-energy collisions and other processes, thereby testing the validity of quantum field theories.

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