I'm a bit confused on the idea of adding corrections to the classical potential of $\phi^4$ theory in QFT. From what I understand is that one should add corrections to the potential in order to calculate the true vacuum (the lowest energy/ the minima of the known potential) in the quantum level. First, is that true? What I don't understand is:
why we regard them as "radiative corrections"?
Why the first order is the sum of all bubbles with external legs? and not other set of diagrams?
And how it relates to the method of weinberg collman to calculate it with the source J? is it because the effective action is the sum of all 1PI diagrams? and again this takes me to the second question why the first correction is the sum of all one bubble diagrams?