DISCRETE-TIME FROM QUANTUM PHYSICS

't Hooft has recently developed a discretization of (2+1) gravity whic h has a multiple-valued Hamiltonian and which therefore admits quantum time evolution only in discrete steps. In this paper, we describe sev eral models in the continuum with single-valued equations of motion in classical physics, but with multiple valued Hamiltonians. Their time displacements in quantum theory are therefore obliged to be discrete. Classical models on smooth spatial manifolds are also constructed with the property that spatial displacements can be implemented only in di screte steps in quantum theory. All these models show that quantizatio n can profoundly affect classical topology.