Empirical success of non-pert methods in QFT?

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In summary, there is empirical support for non-perturbative methods being successfully applied in QFT. Low-energy QCD has seen success in using np-methods for confinement, chiral symmetry breaking, and hadron mass generation. Additionally, effective theories like chiral perturbation theory have also been useful, although they may not be strictly considered np-methods. Instantons and solitons have also been experimentally verified in various areas of physics. While there may be debates about the exact nature of non-perturbative techniques, it is clear that they have played a crucial role in understanding many phenomena in QFT.
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metroplex021
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Someone said at a conference today that there was no empirical support whatsoever for the idea that non-perturbative methods could be successfully applied in QFT. Does anyone know any counterexamples to this claim? I don't work in this area, but it sure doesn't sound right to me...

Any info gratefully received!
 
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In low-energy QCD both analytical and numerical results are obtained via np-methods for mechanisms of confinement, chiral symmetry breaking and hadron mass generation. The biggest success is the application of lattice QCD to hadron spectroscopy with afaik approx. 5% error for hadron masses.

Strictly speaking low-energy effective theories like chiral perturbation theory, heavy baryons etc. are not np-methods as these models are not derived explicitly via integrating out high-energy d.o.f. but in a wider sense they are something like np-methods as well. In 1+1 dim. theories such methods ca be related to the full theory rigorously.
 
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  • #3
Yes, that's complete nonsense, depending of course on what he meant exactly.

Instanton's are the analogue of tunneling effects in quantum mechanics, which is of course well tested. They are ubiqitous in the study of anomalies, as well as in QCD and other areas of particle physics. A good example would be the physics of the Eta prime particle, which Witten solved using nonperturbative physics.

There are many examples of experimentally verified solitons in condensed matter physics.

As far as other nonperturbative techniques. Well, in some sense the Dyson gas technique is known to be correct in describing 2 dimensional plasmas.
 
  • #4
Very good examples, especially the relation anomaly - instanton - eta-prime mass; for the latter only the anomay and therefore only a non-perturbative method can provide an explanation

(many people think that the anomaly is purely perturbative due to the triangle in one loop; this is completely nonsense; it's like saying that every blue paint is heaven b/c the color of heaven is blue)
 
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  • #5
The whole treatment of symmetry broken states is non-perturbative to start with.
 
  • #6
DrDu said:
The whole treatment of symmetry broken states is non-perturbative to start with.
yes, but in many cases it's a classical ground state around which one uses standard perturbation theory
 

1. What is the definition of "non-perturbative methods" in QFT?

Non-perturbative methods in QFT refer to techniques used to solve quantum field theory problems without relying on a perturbative expansion. This means that the calculations are not based on small, incremental changes from a known solution, but rather approach the problem as a whole.

2. How do non-perturbative methods differ from perturbative methods in QFT?

Non-perturbative methods differ from perturbative methods in that they do not rely on approximations and small corrections to a known solution. Instead, they aim to solve the problem as a whole, often through numerical simulations or analytical techniques.

3. What are some examples of non-perturbative methods used in QFT?

Examples of non-perturbative methods in QFT include lattice field theory, which uses a discrete grid to approximate the continuous spacetime of quantum field theory, and the renormalization group, which studies the behavior of systems at different scales.

4. What are the advantages of using non-perturbative methods in QFT?

Non-perturbative methods allow for the study of systems that cannot be solved using perturbative techniques, such as strongly interacting systems. They also provide a more complete understanding of the underlying physics and can accurately describe phenomena at all energy scales.

5. What are the current challenges in achieving empirical success with non-perturbative methods in QFT?

One of the main challenges in achieving empirical success with non-perturbative methods in QFT is the computational complexity of these techniques. Many of these methods require extensive numerical simulations, which can be time-consuming and resource-intensive. Additionally, the development of new and more efficient techniques is an ongoing challenge in this field.

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