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Scalar-Field Interactions in Bohmian Quantum Field Theory Deterministic Particle Dynamics with a Yukawa Mediator

Kevin Bleep

Published Mar 13, 2026• 0 citations
Publisher

Abstract

This paper introduces a deterministic, scalar-mediated extension of Bohmian Quantum Field Theory (QFT). By incorporating a dynamical scalar field into the primitive ontology of the theory, we provide a framework where fermionic particles interact via a Yukawa mediator while following definite trajectories.
DOI
10.5281/zenodo.19009040

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We show how one can reproduce the state evolution known from interacting QFT from an ontological deterministic theory. This is an important step in finding the reality that underlies QFT.In previous work ontic theories behind free QFTs were found, for all QFTs that occur in the Standard Model (spin-0, spin-1/2 & spin-1). In this paper we extend the ontological theory behind QFT to the case with interactions. We do this by starting out from the ontic theories found for free QFTs and see what happens if we try to include interactions (known from QFT). This will lead us to the conjecture that the ontic theory behind any QFT with interaction is, at the basis, the corresponding classical field theory. We study such a classical field theory for the case of a real scalar field with φn-interaction. We determine the evolution of the probability density of the ontic fields and cast it into a formalism known from QFT. We will focus on the simplest case of self-interaction, to illustrate our procedure. We find that we can reproduce the probability evolution from real scalar QFT with (self-)interaction, for this simplest case.
We propose a minimal effective field theory extension of Bohmian mechanics via a weak real Lorentz-scalar field φ coupled to the Dirac bilinear ψ-barψ through a strictly dimensionless Yukawa coupling g. In the non-relativistic limit this adds a classical term gφ(x) directly to the Bohmian quantum potential, Q_eff = Q + gφ(x). The model is fully relativistic, Lagrangian-based, and observationally equivalent to standard quantum mechanics plus a classical Yukawa fifth force. The paper derives the field equations, exact sourced scalar field, conservation laws, and realistic laboratory predictions for atom/neutron interferometry (μeV benchmark) and Casimir forces (meV benchmark). Current bounds already constrain |g| ≲ 10^{-12}–10^{-15}; next-generation experiments can test the predictions. This construction — giving the quantum potential an explicit hidden-sector scalar origin while remaining fully testable by existing fifth-force searches — is original and has not appeared in the literature.
We propose a minimal effective field theory extension of Bohmian mechanics via a weak real Lorentz-scalar field φ coupled to the Dirac bilinear ψ-barψ through a strictly dimensionless Yukawa coupling g. In the non-relativistic limit this adds a classical term gφ(x) directly to the Bohmian quantum potential, Q_eff = Q + gφ(x). The model is fully relativistic, Lagrangian-based, and observationally equivalent to standard quantum mechanics plus a classical Yukawa fifth force. The paper derives the field equations, exact sourced scalar field, conservation laws, and realistic laboratory predictions for atom/neutron interferometry (μeV benchmark) and Casimir forces (meV benchmark). Current bounds already constrain |g| ≲ 10^{-12}–10^{-15}; next-generation experiments can test the predictions. This construction — giving the quantum potential an explicit hidden-sector scalar origin while remaining fully testable by existing fifth-force searches — is original and has not appeared in the literature.