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

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

2009-02-18

arxiv.org/abs/0902.3050v3

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, 13 figures, a minor clarification, references added

Scientific paper

We investigate the unitarity of three dimensional noncommutative scalar field theory in the Lie algebraic noncommutative spacetime [x^i,x^j]=2i kappa epsilon^{ijk}x_k. This noncommutative field theory possesses a SL(2,R)/Z_2 group momentum space, which leads to a Hopf algebraic translational symmetry. We check the Cutkosky rule of the one-loop self-energy diagrams in the noncommutative phi^3 theory when we include a braiding, which is necessary for the noncommutative field theory to possess the Hopf algebraic translational symmetry at quantum level. Then, we find that the Cutkosky rule is satisfied if the mass is less than 1/(2^(1/2)kappa).

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