Is Perturbative Theory Meaningless in Some Cases Despite Small Interaction?

In summary, the perturbative theory is a mathematical approach used in physics to calculate the effects of small interactions on a system. It involves breaking down the problem into smaller, solvable parts and then combining them to find the overall solution. This method is most effective when the interactions are small enough to be considered negligible and the system can be approximated as a sum of smaller, independent parts. However, it may not always give accurate results, especially when the interactions become larger or more complex. Scientists determine the applicability of the perturbative theory by considering the strength and type of interactions in the system, as well as any known correlations between the particles, and may also use numerical simulations or experimental data for validation.
  • #1
ndung200790
519
0
Please teach me this:
Because perturbative QTF theory is an asymptotic theory,then when the series is divergent(the terms of series increase as the n(the number of terms) tend to infinite) I wonder whether the theory is meaningfull or meaningless.
Thank you very much in advanced.
 
Physics news on Phys.org
  • #2


It's meaningful when you take only a few terms of the expansion, but meaningless if you take them all.
 
  • #3


Then,with very large error(despite of taking a few terms in series),why it is still meaningfull?
 
  • #4


Sometimes the error is small, which is why sometimes it's meaningfull.
 

FAQ: Is Perturbative Theory Meaningless in Some Cases Despite Small Interaction?

What is the perturbative theory and how does it work?

The perturbative theory is a mathematical approach used in physics to calculate the effects of small interactions on a system. It involves breaking down the problem into smaller, solvable parts and then combining them to find the overall solution. This method is commonly used when the interactions between particles are small enough to be considered negligible, and the system can be approximated as a sum of smaller, independent parts.

Can the perturbative theory be applied to all systems?

No, the perturbative theory is only applicable to certain systems where the interactions are small enough to be considered negligible. In some cases, the interactions may be too large or complex for the perturbative approach to be accurate.

Is the perturbative theory always accurate?

No, the perturbative theory is an approximation method and may not always give accurate results. It is most accurate when the interactions are small and the system can be approximated as a sum of smaller, independent parts. However, as the interactions become larger or more complex, the accuracy of the perturbative approach decreases.

Are there any cases where the perturbative theory is meaningless?

Yes, there are cases where the perturbative theory may be meaningless despite the interactions being small. This can happen when the system is highly non-linear or when there are strong correlations between the particles, making it difficult to accurately approximate the system as a sum of smaller parts.

How do scientists determine if the perturbative theory is applicable to a specific system?

Scientists usually consider the strength and type of interactions in the system, as well as any known correlations between the particles, to determine if the perturbative theory can be applied. They may also use numerical simulations or experimental data to validate the results obtained from the perturbative approach.

Similar threads

How to demonstrate the asymptotic charateristic of perturbative QTF Theo?
Replies
3
Views
1K
Can we attain a disire approxomation for asymptotic perturbative QTF Theo?
Replies
1
Views
1K
I More doubts in perturbation theory
Replies
8
Views
1K
Why QFT is asymptotic theory but still being very useful?
Replies
5
Views
3K
How to explain the smallness of mass while the mass parameter diverge rapidly in ?
Replies
7
Views
2K
How QTF Theory solves the infinite electromagn selfenergy of electron?
Replies
2
Views
2K
Can we demontrate the convergence of perturbation quantum field theory?
Replies
5
Views
3K
A Structure of Matter in Quantum Field Theory
3
Replies
75
Views
8K
Why we know the renormalization work to all order in renormalizable theory?
Replies
6
Views
3K
A Higgs inflation and quadratic gravity
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top