Causality in non-commutative quantum field theories

Abstract

We study causality in noncommutative quantum field theory with a space–space noncommutativity. 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 the T* product and the T product as a condition of causality violation for a spacelike separation. We discuss two examples; one in a scalar theory and another in the Yukawa theory. In particular, in the context of a noncommutative Yukawa theory, with the interaction Lagrangian , is observed to be causality violating even in the case of space–space noncommutativity for which θ0i = 0.