Why QFT is asymptotic theory but still being very useful?

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Discussion Overview

The discussion revolves around the utility of perturbative quantum field theory (QFT) despite its classification as an asymptotic theory. Participants explore the implications of asymptotic series, the role of Feynman diagrams, and the relationship between low-order approximations and non-perturbative approaches.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions the usefulness of perturbative QFT, noting that asymptotic series often do not converge, which could lead to significant errors.
  • Another participant suggests that the initial terms of an asymptotic series can provide a good approximation, despite the series not converging.
  • A different viewpoint posits that including more Feynman diagrams (higher-order terms) should yield more accurate calculations, yet this contradicts the nature of asymptotic QFT where higher-order terms may be less accurate.
  • One participant introduces the idea that non-perturbative QFT, such as lattice QFT, may represent a more accurate reality than perturbative approaches.
  • A question is raised about how to verify the "good" approximation at low-order terms in asymptotic series, highlighting potential flaws in the application of asymptotic series in QFT.
  • Another participant discusses the renormalization problem in perturbative QFT and suggests that "compensation" among terms in the perturbation series contributes to its asymptotic nature, while still allowing for good approximations at lower orders.

Areas of Agreement / Disagreement

Participants express differing views on the effectiveness of perturbative QFT and the implications of asymptotic series. There is no consensus on the verification of approximations or the superiority of non-perturbative approaches.

Contextual Notes

Limitations include the unclear verification methods for low-order approximations and the unresolved nature of the renormalization problem in perturbative QFT.

ndung200790
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Please teach me this:
Why perturbative QFT is still very useful theory?.Because perturbative QFT is asymptotic theory,so in many cases the series do not converge,then the error might be very large.
Thank you very much for your kind helping.
 
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Because in an asymptotic series a few lowest terms of the expansion represent a good approximation.
 
It seem to me that each Feynman diagram is a possible process.So If our considering includes more and more the diagrams(considering up to higher order terms in the series of perturbation) then our calculation is more and more exactly.But this considering is contrary with asymptotic QFT.(in the asymptotic series,at higher order,then it is the less exactly).So I do not understand where is the reality of the problem.
 
The reality is in non-perturbative QFT, such as lattice QFT.
 
So what is the verification of the ''good'' approximation at low order terms in asymptotic series?Because there is a flaw in the posing the asymptotic series in QFT.
 
It seem that:By perturbation procedure in QFT,the renormalization problem appears.In addition,by the procedure,there are also exist ''compensation things'' appearing among the terms of perturbation series.The compensation values are the cause of the asymptotic characteristic,but at lower order terms of the series,they influence on the terms not much.So at lower order terms,we have a good approximation.Is that correct?
 

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