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We investigate the unitarity of three dimensional noncommutative scalar fieldtheory in the Lie algebraic noncommutative spacetime [x^i,x^j]=2i kappaepsilon^{ijk}x_k. This noncommutative field theory possesses a SL(2,R)/Z_2group momentum space, which leads to a Hopf algebraic translational symmetry.We check the Cutkosky rule of the one-loop self-energy diagrams in thenoncommutative phi^3 theory when we include a braiding, which is necessary forthe noncommutative field theory to possess the Hopf algebraic translationalsymmetry at quantum level. Then, we find that the Cutkosky rule is satisfied ifthe mass is less than 1/(2^(1/2)kappa).

The Cutkosky rule of three dimensional noncommutative field theory in Lie algebraic noncommutative spacetime