Ontological States in Non-Interacting Quantum Field Theories

TL;DR

The paper investigates the possibility of an ontological deterministic underpinning for non-interacting quantum field theories in the Standard Model by constructing explicit ontic states whose beables are fully known and whose time evolution is deterministic. It provides a concrete set of ontic states for real free scalar fields, complex scalars, massless Dirac fermions, and vector bosons, with the evolution of ontic configurations realized as permutations within a well-defined Hilbert-space basis. Each sector is equipped with corresponding beables, ensuring the ontic states form an orthogonal, complete basis that spans the full Hilbert space. This work constitutes a first step toward a deterministic ontology for QFTs, clarifying what constitutes ontic states in free theories and outlining the challenges and necessary steps to include interactions and measurement within such a framework. The results lay groundwork for future attempts to derive Standard Model physics from an underlying ontological theory and motivate further exploration of how such a theory could account for quantum phenomena and observed measurement statistics.

Abstract

This is a paper in the field of ontological deterministic theories behind Quantum Field Theories, like for example the cellular automaton theories proposed by 't Hooft. In these theories one has ontological states in which the state of reality is exactly known and no uncertainties are present. Also these states evolve in time deterministically. A first step in finding the ontological deterministic theory behind the Standard Model is to find in Quantum Field Theory the states that behave as ontological states. We present the ontological states for all non-interacting (3+1-dimensional) Quantum Field Theories occurring in the Standard Model. We summarize the ontological states for free scalar bosons and for free masless Dirac fermions, which are known from the literature. We construct the ontological states for vector bosons, in analogy to the scalar boson case. With this we have a set of ontological states for all particles that are known to occur in reality and in the Standard Model.