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The interaction vertex for a fermionic first order system of weights (1,0)such as the twisted bc-system, the fermionic part of N=2 string field theoryand the auxiliary \eta\xi system of N=1 strings is formulated in the Moyalbasis. In this basis, the Neumann matrices are diagonal; as usual, theeigenvectors are labeled by \kappa\in\R. Oscillators constructed from theseeigenvectors make up two Clifford algebras for each nonzero value of \kappa.Using a generalization of the Moyal-Weyl map to the fermionic case, we classifyall projectors of the star-algebra which factorize into projectors for each\kappa-subspace. At least for the case of squeezed states we recover the fullset of bosonic projectors with this property. Among the subclass of ghostnumber-homogeneous squeezed state projectors, we find a single class ofBPZ-real states parametrized by one (nearly) arbitrary function of \kappa. Thisclass is shown to contain the generalized butterfly states. Furthermore, weelaborate on sufficient and necessary conditions which have to be fulfilled byour projectors in order to constitute surface states. As a byproduct we findthat the full star product of N=2 string field theory translates into acanonically normalized continuous tensor product of Moyal-Weyl products up toan overall normalization. The divergent factors arising from the translation tothe continuous basis cancel between bosons and fermions in any even dimension.Comment: LaTeX, 1+23 pages, minor improvements, references adde

String Field Theory Projectors for Fermions of Integral Weight