QFT & Bound States: Is Calculation Possible?

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Discussion Overview

The discussion centers around the capabilities of quantum field theory (QFT) in calculating and predicting bound states, particularly in the context of strong interactions and hadron masses. Participants explore the limitations of QFT and the potential of alternative approaches like lattice QCD.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Exploratory

Main Points Raised

  • Some participants suggest that QFT does not satisfactorily allow for calculations of bound states, raising concerns about its fundamental nature.
  • Others argue that QFT can successfully address certain problems related to bound states, citing examples like the Lamb shift in light atoms.
  • It is noted that in the case of strong interactions, perturbation theory fails for low energy states, complicating calculations of hadron masses.
  • Participants mention lattice QCD as a non-perturbative approach that can provide estimates for hadron masses, although these solutions are described as being far from exact.
  • One participant seeks clarification on whether lattice QCD refers to non-perturbative QFT or infrared QCD.
  • Another participant provides a brief overview of how lattice QCD operates, emphasizing its method of sampling field configurations based on the action.
  • A minor correction is made regarding the spelling of "hadron," highlighting the importance of precise terminology in scientific discussions.

Areas of Agreement / Disagreement

Participants express differing views on the effectiveness of QFT for bound state calculations, with some asserting its limitations while others point to specific successes. The discussion remains unresolved regarding the overall capability of QFT in this area.

Contextual Notes

There are unresolved issues regarding the applicability of perturbation theory in strong interactions and the exact nature of the solutions provided by lattice QCD. The discussion also reflects varying levels of familiarity with terminology and concepts among participants.

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I read somewhere that quantum field theory does not allow calculations and predictions of bound states in a satisfactory way. Is that true and how much is that a problem given that qft claims to be so fundamental?
 
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As far as i know, QFT does a good job in some problems concerning bound states, e.g. the Lamb shift in light atoms, which has been calculated using QFT in Weinberg's book. But in bound states with strong interaction, as a bound state is a low energy state(~MeV), the strong interaction becomes so strong that perturbation theory breaks down in any sense. So we can't use common QFT method to calculate hadron mass, etc. But we do have some approaches to settle this problem, e.g. lattice QCD, but the solution is far from exact.
 
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wangyi said:
But in bound states with strong interaction, as a bound state is a low energy state(~MeV), the strong interaction becomes so strong that perturbation theory breaks down in any sense. So we can't use common QFT method to calculate hardon mass, etc.

Well this problem is more general. The entire QCD field theory suffers from it.

But we do have some approaches to settle this problem, e.g. lattice QCD, but the solution is far from exact.

Lattice QCD ? You mean non perturbative QFT or infrared QCD, right ?

regards
marlon
 
I hear Lattice QCD can do some non perturbative calculations, for example, it can give hadron mass up to a few percent in most sence. In lattice QCD, we can begin with the Euclidean but entire action, take the action as a probable denisty of all field configurations, place space on lattice and do sampling according to the action.

It's my understanding. I hope it is helpful.

regards.
 
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wangyi, I believe what you say is true. BTW the particle name you want is hadron, with the d coming before the the r. It is important to observe this silly detail because your original spelling has an embarassing slang meaning.
 
Sorry, My mother language is not English, but I will pay more attention on these details. Thank you for your correction.
 

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