Non-anticommutative Supersymmetric Field Theory and Quantum Shift

Details Non-anticommutative Supersymmetric Field Theory and Quantum Shift Non-anticommutative Supersymmetric Field Theory and Quantum Shift

2006-04-05

arxiv.org/abs/hep-th/0604029v2

Phys.Lett.B639:124-134,2006

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, references added, correction made, minor changes made and discussion added in section 5

Scientific paper

10.1016/j.physletb.2006.06.015

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-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.

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