How many Feynman diagrams do I draw?

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SUMMARY

The discussion centers on the necessity of drawing Feynman diagrams for calculating interaction amplitudes in quantum field theory, specifically referencing Tong's lecture notes. For nucleon-nucleon scattering, two diagrams are required due to the flipping of outgoing momentum labels, while meson-meson scattering, particularly the process \(\phi \phi \to \phi \phi\), only necessitates a single diagram. The confusion arises from the lack of clarity on why a second diagram is not needed in the meson case, especially without employing Dyson's formula. Understanding the distinctions between different types of mesons is crucial for grasping this concept.

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mjordan2nd
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I'm currently going through the interaction part of Tong's lecture notes on quantum field theory, and I'm a bit confused about how many Feynman diagrams I need to draw in order to compute the amplitude of various interaction terms. Tong presents Feynman diagrams through a series of examples. For instance for nucleon-nucleon scattering Tong draws two diagrams, with the labels for the outgoing momentum flipped on one diagram with respect to the other. However for meson-meson scattering there is a single diagram. Why don't we need a second diagram in the meson-meson case with the labels of the outgoing momentum flipped on the second diagram? I don't understand how to see this without using Dyson's formula.
 
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Two different mesons?
More context would help.
 
The meson scattering I'm looking at is indeed \phi \phi \to \phi\phi.
 

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