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.

Read more about this topic:  Yukawa Potential

Famous quotes containing the word transform:

    “Americans, unhappily, have the most remarkable ability to alchemize all bitter truths into an innocuous but piquant confection and to transform their moral contradictions, or public discussion of such contradictions, into a proud decoration, such as are given for heroism on the battle field.”
    —James Baldwin (1924–1987)