Commutators and propagators of Moyal star-products and microcausality   for free scalar field on noncommutative spacetime
  We study the Moyal commutators and their expectation values between vacuum states and non-vacuum states for free scalar field on noncommutative spacetime. Then from the Moyal commutators, we find that the microcausality is satisfied for the linear operators of the free scalar field on noncommutative spacetime. We construct the Feynman propagator of Moyal star-product for noncommutative scalar field theory. 
Zheng Ze Ma