Crypto-Hermiticity of nonanticommutative theories
  We note that, though nonanticommutative deformations of Minkowski supersymmetric theories do not respect the reality condition and seem to lead to non-Hermitian Hamiltonians H, the latter belong to the class of crypto-Hermitian (or quasi-Hermitian) Hamiltonians having attracted recently a considerable attention.   They can be made manifestly Hermitian via the similarity transformation H -> e^R H e^{-R} with a properly chosen R. The deformed model enjoys the same supersymmetry algebra as the undeformed one though it is difficult in some cases to write explicit expressions for a half of supercharges. The deformed SQM models make perfect sense. It is not clear whether it is also the case for NAC Minkowski field theories -- the conventionally defined S--matrix is not unitary there. 
A.V. Smilga