  Space-time non-commutative theories are non-local in time. We develop the
Hamiltonian formalism for non-local field theories in d space-time dimensions
by considering auxiliary d+1 dimensional field theories which are local with
respect to the evolution time. The Hamiltonian path integral quantization is
considered and the Feynman rules in the Lagrangian formalism are derived. The
case of non-commutative \phi^3 theory is considered as an example.
