Some Doubts on Perturbation theory

In summary, the conversation discusses the possibility of a non-renormalizable theory in three or four dimensions being renormalizable in two dimensions, specifically in the case of gravity. The conversation also touches on the use of perturbation theory and its relation to covariant perturbation theory. It is mentioned that gravity may not be renormalizable in any dimension, but it is exactly solvable in (2+1) dimensions.
  • #1
eljose79
1,518
1
Here they go my doubts:

a)Could It be that a theroy that is not renormalizable in three or four dimension could it be renormalizaed in two?..i mean if depending on the dimension a theory is renormalizable or not...when it comes to gravity..in which dimension is renormalizable?.

b)When you have HF=dF/dt where this would be the functional schroedinguer equation with functional derivatives then if we have H=H0+Hint then if we use perturbation theory to calculate F (The functional wave)..my question if that this perturbation scheme is realted to the covariant perturbation theory.
 
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  • #2
I don't know why you said doubts, but

1. Yes. Renormalizability depends on dimension of spacetime. It is essentially because power counting of momenta for your propagators depends on it. I don't know in what dimension gravity is renormalizable (It may not be in any dimension), but in (2+1) dimension it is exactly solvable even though it is not renormalizable.

2. In principle, yes.

Instanton
 

1. What is perturbation theory?

Perturbation theory is a mathematical technique used to approximate solutions to complex problems by breaking them down into simpler, solvable components.

2. When is perturbation theory used?

Perturbation theory is commonly used in physics, engineering, and other scientific fields to solve problems that cannot be solved exactly using traditional methods.

3. What are some common doubts about perturbation theory?

Some common doubts about perturbation theory include its reliability in providing accurate solutions, its applicability to all types of problems, and the level of complexity it can handle.

4. How does perturbation theory work?

Perturbation theory works by assuming that a problem can be broken down into a solvable part and a perturbation, or small deviation from the solvable part. The perturbation is then treated as a small correction to the solution of the simplified problem.

5. What are the limitations of perturbation theory?

While perturbation theory can provide useful approximations in many cases, it may not always yield accurate results. It also relies on the problem being solvable in simpler terms and may not be applicable to highly complex or nonlinear systems.

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