Lorentz invariant and supersymmetric interpretation of noncommutative quantum field theory

In this paper, based on recent work [13] 1 , we construct deformed Poincaré SUSY algebra in terms of twisted (Hopf) algebra. By adapting this new interpretation of superPoincaré algrebra as our fundamental symmetry, we can construct Lorentz and Poincaré SUSY invariant quantum field theory on the non(anti)commutative (super)space. The key point is validity of our new twist element that guarantees non(anti)commutativity of space. It is checked in this paper for N = 1 case. We also comment on the possibility of noncommutative central charge coordinate. E-mail : [email protected] E-mail : [email protected] After submitting the first version of this paper to hep-th arXiv., we have received a notice from R. Oeckl that he had given his paper [29], which covers almost all result in [13].