In this talk we present a field theoretical model constructed in Minkowski [Formula: see text] superspace with a deformed supercoordinate algebra. Our study is motivated in part by recent results from super-string theory, which show that in a particular scenario in Euclidean superspace the spinor coordinates θ do not anticommute. Field theoretical consequences of this deformation were studied in a number of articles. We present a way to extend the discussion to Minkowski space, by assuming non-vanishing anticommutators for both θ, and [Formula: see text]. We give a consistent supercoordinate algebra, and a star product that is real and preserves the (anti)chirality of a product of (anti)chiral superfields. We also give the Wess-Zumino Lagrangian [Formula: see text] that gains only Lorentz-invariant corrections due to non(anti)commutativity within our model. The Lagrangian in Minkowski superspace is also always manifestly Hermitian.
A Possible Field-Theoretical Model of Quark Confinement
