Physical degrees of freedom of non-local theories

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, (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 = 1/g 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 = M-2/g. (C) 2004 Elsevier B.V. All rights reserved.