Determinism and a supersymmetric classical model of quantum fields

TL;DR

This paper presents a supersymmetric classical model that reproduces quantum field theory dynamics through a positivity constraint, supporting 't Hooft's idea of quantum mechanics emerging from deterministic systems.

Contribution

It introduces a supersymmetric classical framework that derives quantum field theory via a positivity constraint, linking classical dynamics to quantum behavior.

Findings

Liouville operator split into positive and negative spectra

Positivity constraint eliminates unstable negative spectrum

Quantum field theory emerges from classical Liouville dynamics

Abstract

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 Schroedinger 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.