  The issue of the existence and possible triviality of the Euclidean quantum
scalar field in dimension 4 is investigated by using some large deviations
techniques. As usual, the field $\varphi_{d}^{4}$ is obtained as a limit of
regularized fields $\varphi_{k}^{4}$ associated with a probability measures
$\mu_{k,V}$, where $k, V$ represent ultraviolet and volume cutoffs. The result
obtained is that in a fixed volume, the almost sure limit (as $k \rightarrow
\infty$) of the density of $\mu_{k,V}$, with respect to the Gaussian free field
measure, exists and is equal to $0$, when the coupling constant is not
vanishing. This implies that $\mu_{k,V}$ can not have a strong limit as the
ultraviolet cutoff is removed. Furthermore, the normalization sequence
$Z_{k,V}=E e^{-{\cal A}_{k,V}}$ is divergent as $k \rightarrow \infty$ for
dimensions $d\geq4$ when the vacuum renormalization is lower than some
threshold, which leads to the non ultraviolet stability of the field in this
case. These assertions are also valid for vector fields and can be extended to
polynomial Lagrangians.
