  We study the $\phi_{\star}^4$ model for a scalar field in a linearization of
the Snyder model, using the methods of the Worldline Formalism. Our main result
is a master equation for the 1-loop n-point function. From this we derive the
renormalization of the coupling parameters of the theory and observe the
appearance of a $\phi^6$ divergent contribution that opens the question of
whether this theory is renormalizable or not. Additionally, we observe that
some terms in the renormalized action can be interpreted as coming from an
effective metric proportional to the square of the field.
