Deterministic models of quantum fields

TL;DR

This paper presents a classical supersymmetric model that, through a specific constraint, reproduces a quantum field theory, offering insights into deterministic foundations of quantum mechanics and potential cosmological implications.

Contribution

It introduces a local supersymmetric classical model whose constrained dynamics yield a genuine quantum field theory, bridging classical and quantum descriptions.

Findings

Classical Liouville equation can be transformed into a functional Schrödinger equation.

A supersymmetric classical model reproduces quantum field theory dynamics.

A gauge theory with varying alpha demonstrates energy-parity symmetry and cosmological constant protection.

Abstract

Deterministic dynamical models are discussed which can be described in quantum mechanical terms. -- In particular, a local quantum field theory is presented which is a supersymmetric classical model. The Hilbert space approach of Koopman and von Neumann is used to study the classical evolution of an ensemble of such systems. Its Liouville operator is decomposed into two contributions, with positive and negative spectrum, respectively. The unstable negative part is eliminated by a constraint on physical states, which is invariant under the Hamiltonian flow. Thus, choosing suitable variables, the classical Liouville equation becomes a functional Schroedinger equation of a genuine quantum field theory. -- We briefly mention an U(1) gauge theory with ``varying alpha'' or dilaton coupling where a corresponding quantized theory emerges in the phase space approach. It is energy-parity symmetric and, therefore, a prototype of a model in which the cosmological constant is protected by a symmetry.