Control of quantum fluctuations for a Yukawa interaction in the Kaluza Klein picture

We study a system of fermions interacting with a scalar field, in 4+1 dimensions where the 5th dimension is compactified, using an exact functional method, where quantum fluctuations are controlled by the amplitude of the bare fermion mass. The integration of our equationsleads to the properties of the dressed Yukawa coupling, that we study at one-loop so as to show the consistency of the approach. Beyond one loop, the non-perturbative aspect of the method gives us the possibility to derive the dynamical fermion mass. The result obtained is cut off independent and this derivation proposes an alternative to the Schwinger-Dyson approach.