  We discuss continuous and discrete sectors in the collective field theory of
$d=1$ matrix models. A canonical Lorentz invariant field theory extension of
collective field theory is presented and its classical solutions in Euclidean
and Minkowski space are found. We show that the discrete, low density, sector
of collective field theory includes single eigenvalue Euclidean instantons
which tunnel between different vacua of the extended theory. We further show
that these ``stringy" instantons induce non-perturbative effective operators of
strength $e^{-{1\over g}}$ in the extended theory. The relationship of the
world sheet description of string theory and Liouville theory to the effective
space-time theory is explained. We also comment on the role of the discrete,
low density, sector of collective field theory in that framework.
