Noncommutative associative superproduct for general supersymplectic   forms
  We define a noncommutative and nonanticommutative associative product for general supersymplectic forms, allowing the explicit treatment of non(anti)commutative field theories from general nonconstant string backgrounds like a graviphoton field. We propose a generalization of deformation quantization a la Fedosov to superspace, which considers noncommutativity in the tangent bundle instead of base space, by defining the Weyl super product of elements of Weyl super algebra bundles. Super Poincare symmetry is not broken and chirality seems not to be compromised in our formulation. We show that, for a particular case, the projection of the Weyl super product to the base space gives rise the Moyal product for non(anti)commutative theories. 
A. De Castro (1), I. Martin (1), L. Quevedo (1), A. Restuccia (1,2)   ((1) Universidad Simon Bolivar, (2) Max Planck Inst. f...