Non-anticommutative supersymmetric field theory and quantum shift

Masato Arai, Masud Chaichian, Kazuhiko Nishijima, Anca Tureanu
2006 Physics Letters B  
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
more » ... we comment the preservation of the (initial) N=1 super-Poincar\'e {\it algebra} and on the consequent super-Poincar\'e invariant interpretation of the discussed model, but also provide a measure for the violation of the super-Poincar\'e symmetry.
doi:10.1016/j.physletb.2006.06.015 fatcat:xcuhjbfnyjai7ctziysqke2oeu