Causality in Non-Commutative Quantum Field Theories

We study causality in non-commutative quantum field theory with a space-space non-commutativity. We employ the S-operator approach of Bogoliubov-Shirkov(BS). We generalize the BS criterion of causality to the noncommutative theory. The criterion to test causality leads to a nonzero difference between T*-product and T-product as a condition of causality violation for a spacelike separation. We discuss two examples; one in a scalar theory and one in the Yukawa theory. In particular, in the context of a non-commutative Yukawa theory, with the interaction Lagrangian $\bar{\psi}(x)\star\psi(x)\star\phi(x)$, is observed to be causality violating even in case of space-space noncommutativity for which \theta^{0i}=0. \