The phase space description of a class of classical supersymmetric Hamiltonian systems is shown to contain the Schroedinger picture of related quantum field theories. A constraint on the Grassmann valued variables selects the quantum mechanical degrees of freedom. Here, the Liouville operator is related to a Hilbert space Hamiltonian with stable groundstate, unlike the case of statistical mechanics studied earlier in the operator approach by Koopman and von Neumann. The phase space constraint could reflect a dynamical symmetry breaking. In this way, a scale is introduced which discriminates the underlying classical behaviour from the emergent quantum features. This illustrates 't Hooft's proposal to reconstruct quantum mechanics as an emergent theory. It is achieved here for an interacting field theory for the first time.