And you just calculate the integral up to a cutoff scale m.Īnd then you have an additional term you have to in principle evaluate from m to infinite. And so you introduce this additional factor here in the integral. So what happens now if we don't just to the integration, but to some scale. And that actually caused this entire theory to not really make much progress for quite some time, because you were not actually able to calculate anything. If you calculate the scattering process, the result is better not infinite.
So the result of the integral is infinity.
And if you have this evaluated at infinite, we find that it diverges. So if you do this, you know that this results in a logarithmic term. And then we have to integrate this from 0 to infinity. So we have an integral, 1 over q to the fourth power, times q to the third power. And if you go to just very large values of q, that's the only thing which remains. If you look at under in this fraction here, we find a q squared times q squared. The first part is this finite element here, which we can rewrite as q cubed times a finite element dq times all the angles which we have to integrate around. And if you were to- and we have all the tools at hand to actually do the calculation- if you were to calculate the amplitude, we find this term here. So if we look at this higher-order diagram here, one of the specific ones where we have a self correction, self energy correction to the propagator C here. What we want to do here is investigate one of the features, a very important features of having those higher-order corrections. And I'm not actually planning to do this in the lecture. We didn't do any of the calculations, or we didn't calculate the Feynman diagram itself. So in the previous video, we talked about higher-order diagrams and we looked at how we can classify those contributions to the total matrix element.
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