Feynman Amplitude
The Yukawa potential can be derived as the lowest order amplitude of the interaction of a pair of fermions. The Yukawa interaction couples the fermion field to the meson field with the coupling term
The scattering amplitude for two fermions, one with initial momentum and the other with momentum, exchanging a meson with momentum k, is given by the Feynman diagram on the right.
The Feynman rules for each vertex associate a factor of g with the amplitude; since this diagram has two vertices, the total amplitude will have a factor of . The line in the middle, connecting the two fermion lines, represents the exchange of a meson. The Feynman rule for a particle exchange is to use the propagator; the propagator for a massive meson is . Thus, we see that the Feynman amplitude for this graph is nothing more than
From the previous section, this is seen to be the Fourier transform of the Yukawa potential.
Read more about this topic: Yukawa Potential
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