Non-anticommutative Supersymmetric Field Theory and Quantum Shift
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-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.
Cite
@article{arxiv.hep-th/0604029,
title = {Non-anticommutative Supersymmetric Field Theory and Quantum Shift},
author = {Masato Arai and Masud Chaichian and Kazuhiko Nishijima and Anca Tureanu},
journal= {arXiv preprint arXiv:hep-th/0604029},
year = {2008}
}
Comments
17 pages, references added, correction made, minor changes made and discussion added in section 5