  The Gaussian-time-dependent variational equations are used to explored the
physics of $(\phi^4)_{3+1}$ field theory. We have investigated the static
solutions and discussed the conditions of renormalization. Using these results
and stability analysis we show that there are two viable non-trivial versions
of $(\phi^4)_{3+1}$. In the continuum limit the bare coupling constant can
assume $b\to 0^{+}$ and $b\to 0^{-}$, which yield well defined asymmetric and
symmetric solutions respectively. We have also considered small oscillations in
the broken phase and shown that they give one and two meson modes of the
theory. The resulting equation has a closed solution leading to a ``zero mode''
and vanished scattering amplitude in the limit of infinite cutoff.
