Renormalizability - how to determine if a theory is renormalizable?

[mhill]

Given a theory with n-different fields $$\phi _{n}(x)$$ and a known Lagrangian L is possible to see at first sight if the theory will be renormalizable or non*-renormalizable ?? , or on the other hand should we calculate ALL the infinite diagramms to see it, for example i give a certain Lagrangian involving scalar particles, spin 1 particles and spin*-2 particles and several coupling constants could you say if this is renormalizable or not ?

 

[genneth]

I doubt that it is simple to see, otherwise it wouldn't have warranted several Nobel Prizes in recognition of showing that various gauge theories are re-normalisable...

 

[lbrits]

Given a theory with n-different fields $$\phi _{n}(x)$$ and a known Lagrangian L is possible to see at first sight if the theory will be renormalizable or non*-renormalizable ?? , or on the other hand should we calculate ALL the infinite diagramms to see it, for example i give a certain Lagrangian involving scalar particles, spin 1 particles and spin*-2 particles and several coupling constants could you say if this is renormalizable or not ?

There are general theorems based on power counting which tell you which theories are NOT renormalizable. You end up with so few remaining that you can just go around testing them one by one, I believe. I think it is pretty well discussed in Peskin and Schroeder.

 

[nrqed]

There are general theorems based on power counting which tell you which theories are NOT renormalizable. You end up with so few remaining that you can just go around testing them one by one, I believe. I think it is pretty well discussed in Peskin and Schroeder.

As far as I know, the only rule of thumb is that operators of dimension 5 and higher are automatically non-renormalizable. Are there any other quick rule?



IF all the terms are of dimension 4 (or less) then a crafeul check must be made.