Nonrenormalizable Quantum Field Models in Four-Dimensional Space-Time

The construction of no-cutoff Euclidean Green's functions for nonrenormalizable interactions ${\mathcal{L}}_I\left(\varphi \right)=\lambda \int d\delta \left(\epsilon \right):\exp \epsilon \varphi :$ in four-dimensional space-time is carried out. It is shown that all axioms for the generating functional of the Euclidean Green's function are satisfied except perhaps SO(4) invariance.