  The $\phi^4$ field model is generalized to the case when the field $\phi(x)$
is defined on a Lie group: $S[\phi]=\int_{x\in G} L[\phi(x)] d\mu(x)$,
$d\mu(x)$ is the left-invariant measure on a locally compact group $G$. For the
particular case of the affine group $G:x'=ax+b,a\in\R_+, x,b \in \R^n$ t he
Feynman perturbation expansion for the Green functions is shown to have no
ultra-violet divergences for certain choice of $\lambda(a) \sim a^\nu$.
