Methods for Non-renormalizable theories?

[eljose79]

I have some doubts when dealing with non-renormalizable theories in fact le,s suppose we have a theory that is non-renormalizable for n>4 or n=4 then we could do the trick of triying to renormalize it in 4-e dimension being e a small parameter e>0 and after that take the limit e=0 (dimensional regularization).

Another way would be to introduce a cut-off in momentum integrate for momentum<R being R the cut-off so the intgrals are function of R after that we would make an expansion through the singularity in R of the function I(R) and the singularities are isolated...


then now after the chat my question is why if these methods exist are still some non-renormalizable theories?...thanks for the reply.

 

[DarMM]

That's just regularizing the integral. To renormalize you also need to have counterterms to absorb the divergences. Non-renormalizable theories have divergences that grow with perturbative order and thus no amount of counterterms will be sufficient.