Do we really need loop diagrams?

[RedX]

Is it really necessary to learn how to calculate loop diagrams in QFT?

In the Wilsonian approach, you only need to calculate tree diagrams.

In the loop approach, you have to relate the experimentally measured coupling constant to the bare coupling constant, and I guess the difficulty is doing this to a high order - you have to calculate many loops.

In the Wilsonian approach, I guess you still have to relate the experimentally measured coupling constant to the bare coupling constant, but instead of getting it to higher order by calculating loops (since there are no loops in the Wilsonian approach), you have to relate the experimental coupling constant to the infinite amount of constants in front of the infinite amount of terms in the Lagrangian.

Which is more difficult, the loop approach or the Wilson approach? Also, which is actually used in practice?

 

[Demystifier]

In the Wilsonian approach, you only need to calculate tree diagrams.

Are you saying that you can determine the effective action without calculating the loops determined by the fundamental action? I don't think that you can do that.

 

[RedX]

Are you saying that you can determine the effective action without calculating the loops determined by the fundamental action? I don't think that you can do that.

What use is the effective action then, if you still have to calculate loops in the fundamental action?

Even if you have the fundamental action, you have to perform renormalization by replacing bare couplings with experimental couplings - in other words, experiment must enter your theory somehow.

Instead, can you guess the form of the effective action, and then match experimental couplings to the coefficients in the effective action by comparing the experimental results with tree diagrams resulting from your guessed form of the effective action?

 

[Demystifier]

What use is the effective action then, if you still have to calculate loops in the fundamental action?

You can calculate the loops ones and for all, derive the effective action from the loops, and then, in all subsequent applications, use the effective action only.

Instead, can you guess the form of the effective action, and then match experimental couplings to the coefficients in the effective action by comparing the experimental results with tree diagrams resulting from your guessed form of the effective action?

Yes, you can do that too. But such an approach is less predictive.