Hamiltonian Formalism for Space-time Non-commutative Theories

Space-time non-commutative theories are non-local in time. We develop the Hamiltonian formalism for field theories in d space-time dimensions by considering an auxiliary d+1 field theory which is local with respect to the extra evolution time. The Hamiltonian path integral quantization is considered. The case of NC $\phi^3$ is considered as an example. The non-unitarity of these theories can be deduced from this analysis.