SUSY anomaly in quantum-mechanical systems

Explicit examples of supersymmetric systems are constructed involving finite numbers of degrees of freedom where the quantum supersymmetry algebra Q2 = 0, {Q,anti Q}+ = H cannot be preserved on the classical level. Resolving the ordering ambiguities in different ways leads either to a modified algebra i{Q,Q}P.B. = i{Q,anti Q}P.B. = H, or to a reduced algebra i{R,R}P.B. = H with R = anti R, or totally destroys supersymmetry. (orig.)