Non-anticommutative Supersymmetric Field Theory and Quantum Shift

Non-anticommutative Grassmann coordinates in four-dimensional twistdeformed N = 1 Euclidean superspace are decomposed into geometrical ones and quantum shift operators. This decomposition leads to the mapping from the commutative to the non-anticommutative supersymmetric field theory. We apply this mapping to the Wess-Zumino model in commutative field theory and derive the corresponding non-anticommutative Lagrangian. Based on the theory of twist deformations of Hopf algebras, we comment the preservation of the (initial) N = 1 super-Poincaré algebra and on the consequent super-Poincaré invariant interpretation of the discussed model, but also provide a measure for the violation of the super-Poincaré symmetry.