QUANTUM-MECHANICS IN DYNAMICAL-SYSTEMS WITH SUPERSYMMETRY ON A CURVED SPACE

The quantization of a dynamical system constrained to a curved space embedded in the higher dimensional Euclidean space is extended to the case that the system holds the supersymmetry. Using the projection-operator method, we show that the resultant Hamiltonian contains the additional terms interpreted as the quantum corrections due to the noncommutativity among the operators, which are completely missed in the usual approach with Dirac's formalism. These quantum corrections are further shown to break at the operator level the supersymmetry, which holds at the classical level.