Yukawa Potential - Fourier Transform

Fourier Transform

The easiest way to understand that the Yukawa potential is associated with a massive field is by examining its Fourier transform. One has

$V(\mathbf{r})=\frac{-g^2}{(2\pi)^3} \int e^{i\mathbf{k \cdot r}} \frac {4\pi}{k^2+m^2} \;d^3k$

where the integral is performed over all possible values of the 3-vector momentum k. In this form, the fraction is seen to be the propagator or Green's function of the Klein-Gordon equation.

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