Does Renormalisability Depend on Spin in Quantum Field Theory?

[ismaili]

Dear all,

I heard that renormalisability has something to do with the spin. A quantum field theory of particles with spin 0 or 1/2 is renormalisable; where with spin 1 is originally unrenormalisable, however, since we have gauge theory for the spin 1 particles, the symmetry cures the problem, and the field theory becomes renormalisable in the case of spin = 1.
In this perspective, a field theory of spin 2 particles is unrenormalizable, like the quantum gravity.

But I haven't read about this from the renormalisation sections of some books, like Ryder or Peskin.
Is this related to the proof provided by 't Hooft?
Or anyone can provide a correct and clear picture or explanation?
Many thanks!

 

[DarMM]

See section 12.1 of Weinberg's "Quantum Theory of Fields, Volume 1".

Although it's basically just Section 10.1 of Peskin and Schroeder. There they obtain formulas for Bosons and Fermions and you can see the vertex terms, i.e. $V$ contains a term depending on the dimensionality of the coupling. It's simply that for the higher spin cases the simplest interacting terms have couplings with negative dimension.