MG11 
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On the path integral for non--commutative theories

For quantum field theories on non-commutative spacetime, it is known that Feynman rules are not equivalent, if time does not commute with space. In particular, the Feynman rules that are derived from the path integral corresponding to the $T^{\star}$--product (the so--called na\"{i}ve Feynman rules) violate both the opitcal theorem as well as time ordering property.\\ Within the Hamiltonian approach to quantum field theory, we show that we can (formally) modify the time ordering encoded in the above path integral. The resulting Feynman rules are identical to those obtained in the canonical approach via the Gell--Mann-Low formula (with T--ordering). They preserve thus unitarity and time ordering property. We comment on related aspects.