  We analyze the physical (reduced) space of non-local theories, around the
fixed points of these systems, by analyzing: i) the Hamiltonian constraints
appearing in the 1+1 formulation of those theories, ii) the symplectic two form
in the surface on constraints.
  P-adic string theory for spatially homogeneous configurations has two fixed
points. The physical phase space around $q=0$ is trivial, instead around
$q=\frac 1g$ is infinite dimensional. For the special case of the rolling
tachyon solutions it is an infinite dimensional lagrangian submanifold. In the
case of string field theory, at lowest truncation level, the physical phase
space of spatially homogeneous configurations is two dimensional around $q=0$,
which is the relevant case for the rolling tachyon solutions, and infinite
dimensional around $q=\frac {M^2}g$.
