On the Implementation of Supersymmetry
  The implementation of supersymmetry transformations by Hilbert space operators is discussed in the framework of supersymmetric C$^*$--dynamical systems. It is shown that the only states admitting such an implementation are pure supersymmetric ground states or mixtures and elementary excitations thereof. Faithful states, such as KMS--states, are never supersymmetric. 
Detlev Buchholz