# Some Doubts on Perturbation theory

1. May 22, 2003

### eljose79

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 wich 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.

2. May 24, 2003

### instanton

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