Determinism and a supersymmetric classical model of quantum fields

A quantum field theory is described which is a supersymmetric classical model. Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The unstable negative part is eliminated by a positivity constraint on physical states, which is invariant under the classical Hamiltonian flow. In this way, the classical Liouville equation becomes a functional Schrödinger equation of a genuine quantum field theory. Thus, 't Hooft's proposal to reconstruct quantum theory as emergent from an underlying deterministic system, is realized here for a field theory. Quantization is intimately related to the constraint, which selects the part of Hilbert space where the Hamilton operator is positive. This is seen as dynamical symmetry breaking in a suitably extended model, depending on a mass scale which discriminates classical dynamics beneath from emergent quantum mechanical behaviour