2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55859The 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.Latex, 9 pages, prose improved, typos correctedHigh Energy Physics - TheoryMathematical Physicstext