Do we really need loop diagrams?

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Discussion Overview

The discussion revolves around the necessity and practicality of calculating loop diagrams in quantum field theory (QFT), particularly in comparison to the Wilsonian approach, which primarily involves tree diagrams. Participants explore the implications of both methods for relating experimental measurements to theoretical models.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants question the necessity of calculating loop diagrams in QFT, suggesting that the Wilsonian approach, which relies on tree diagrams, may suffice.
  • Others argue that the effective action cannot be determined without considering loops from the fundamental action, raising concerns about the utility of the effective action if loops are still required.
  • There is a discussion on the process of renormalization, where participants note that experimental couplings must be incorporated into the theory, regardless of the approach taken.
  • Some propose that one could guess the form of the effective action and match experimental couplings to its coefficients, although this method is described as less predictive.
  • Participants express differing views on whether the loop approach or the Wilsonian approach is more difficult or more commonly used in practice.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the necessity of loop diagrams versus the Wilsonian approach, with multiple competing views remaining on the effectiveness and practicality of each method.

Contextual Notes

There are unresolved questions regarding the relationship between effective actions and fundamental actions, as well as the implications of renormalization in both approaches. The discussion highlights the complexity of relating theoretical models to experimental results.

RedX
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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?
 
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RedX said:
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.
 
Demystifier said:
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?
 
RedX said:
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.

RedX said:
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.
 

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