  The $U_L(3)\times U_R(3)$ Linear Sigma Model (LSM) with quark degrees of
freedom is used to show that radiative corrections generate undetermined finite
contributions. Their origin is related to surface terms which are differences
between divergent integrals with the same degree of divergence. The technique
used to detect these ambiguities is an implicit regularization on basic
divergent integrals that do not depend on external momenta. We show that such
contributions are absorbed by renormalization or fixed by symmetry
requirements. The general expression for surface terms is derived.
Renormalization group coefficients are calculated, as well as relevant
observables for this model, such as $f_{\pi}$, $f_k$ and the pion and kaon form
factors.
