Nonlinear supersymmetry: from classical to quantum mechanics

Quantization of the nonlinear supersymmetry faces a problem of a quantum anomaly. For some classes of superpotentials, the integrals of motion admit corrections guaranteeing the preservation of the nonlinear supersymmetry at the quantum level. With an example of a system realizing the nonlinear superconformal symmetry, we discuss the nature of such corrections and speculate on their possible general origin.