Renormalization of the $SU_3\otimes SU_3$-$\sigma$-model for $0^{\pm}$-mesons with linear breaking

Ward identities are deduced for divergent Green's functions in the framework of the $SU_3$-$\sigma$-model for $0^{\pm}$-mesons with linear breaking. The model is renormalized. A diagrammatic technique is obtained for the renormalized perturbation series and the propagators and vertices are constructed in the one-loop approximation. Equations are also obtained for the tadpole contributions and the stability conditions are analyzed. The validity of the Goldstone theorem in the one-loop approximation is verified.