Initial value problem in string-inspired nonlocal field theory

We consider a nonlocal scalar field theory inspired by the tachyon action in open string theory. The Lorentz-covariant is characterized parameter $\xi^2$ that quantifies amount of nonlocality. Restricting to purely time-dependent configurations, we show redefinition perturbative reduces local two-derivative with $\xi^2$-dependent potential. This picture supported evidence maps wildly oscillating rolling solutions conventional new For general configurations exhibit an obstruction formulation, but can still achieve formulation time, as well light-cone formulation. These constructions provide initial value and Hamiltonian. Their causality consistent lack superluminal behavior