Determinism and a supersymmetric classical model of quantum fields

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 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.

Can quantum mechanics be an emergent phenomenon?

“…Applications of the outlined scenario have been given, e.g., in Refs. [11,12,13,14,15]. For other approaches see also Refs.…”

Quantum properties of a cyclic structure based on tripolar fields

“…On the other hand, there are models showing that a classical system can manifest itself quantummechanically [11], which means that quantum field theories could be underlied by classical mechanics [12], with quantum uncertainties also having a deterministic origin [13]. Many physicists explore the possibility that quantum phenomena could arise as a result of information loss due to non-reversible dissipative processes and self-organisation in nonlinear deterministic systems [14].…”

A Relativistic Gauge Theory of Nonlinear Quantum Mechanics and Newtonian Gravity

“…Part of the motivation for the present work comes from recent considerations of the possibility of a deterministic foundation of quantum mechanics, as it has already been verified in a number of models [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. While general principles and physical mechanisms ruling the construction of a deterministic classical model underlying a given quantum field theory are hard to come by, cf.…”