proved the so called reconstruction theorem [@ConnesRec] for commutative spectral triples satisfying various axioms, showing that exists a compact oriented smooth manifold $X$ such that $A = C^\infty(X)$ is the algebra of smooth functions on $X$ and every compact oriented smooth manifold emerges in this way. Pushed by the aim of reformulating the standard model of particles in a non-commutative way [@Connes2; @Connes3], Connes has introduced the almost-commutative spectral triple extending the axioms of the reconstruction theorem to a non-commutative algebra. A first attempt to formulate a field theory for a truly non-commutative algebra was obtained replacing in the usual field theory action the point-wise multiplication of the fields with a non-commutative one, namely a $\star$-product. The fields now belongs to $\mathbb{R}^4_\Theta$, a vector space defined by an enough regular class functions on $\mathbb{R}^4_\Theta$ equipped with the Moyal product: $$(f \star g)(x) = \int \int d^4 y \frac{d^4 k}{(2\pi)^4} f(x+\frac{1}{2}\Theta \cdot k) g(x+y) e^{i\langle k,y\rangle}$$ Where $\Theta$ is a skew-symmetric matrix. A very important question about non-commutative quantum field theory [@ncft3], is whether or not the quantum theory is well-defined or in other words if it is renormalizable or not. At first sight, the non-locality of the non-commutate action induced 