Non-anticommutative Supersymmetric Field Theory and Quantum Shift
arXiv:hep-th/0604029 · doi:10.1016/j.physletb.2006.06.015
Abstract
Non-anticommutative Grassmann coordinates in four-dimensional twist-deformed 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 {\it 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.
17 pages, references added, correction made, minor changes made and discussion added in section 5
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