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.
 
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  • #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?

1. 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.

2. 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.

3. 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.

4. 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.

5. 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.

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