Fine structure constant and perturbation theory

[asimov42]

Hi all,

I have a question about perturbation theory and the fine structure constant. Consider an electron moving through the vacuum - this wil induce vacuum polarization, and (if I understand correctly) perturbation theory can be used to analyze the situation. My question is essentially: if the fine structure constant took on a different value (as some theories predict is can), would the interaction between the electron field and the electromagnetic field be different? That is, would you draw a different sequence of Feynman diagrams for the different cases (alpha_1 vs. alpha_2) - does changing the strength of the electromagnetic interaction change the perturbative (or non-perturbative) result?

Thanks!

 

[mfb]

You would draw the same sets of diagrams, but their relative strength (at different orders of alpha) would vary. With a smaller alpha, higher orders would have less influence, and with a large alpha, a lot of different diagrams would contribute significantly.

You can see this at the strong force: It has a large coupling constant, and perturbative calculations are much more difficult there.