Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0906.1723 · Annals of Physics

Quantization in classical mechanics and its relation to the Bohmian Ψ-field

V. D. Rusov, D.S. Vlasenko, S.Cht. Mavrodiev

Published Apr 22, 2011• 11 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2011.04.012

Related papers

Covariant canonical quantization of fields and Bohmian mechanics

H. Nikolić

arXiv:hep-th/0407228•The European Physical Journal C•Jul 6, 2005•14 citations

The Scalar Field Extension of Bohmian Mechanics: An Effective Field Theory with Laboratory-Testable Predictions

Kevin Bleep

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.

•Mar 11, 2026•0 citations

Quantization of classical mechanics: Shall we lie?

Maria Clara Nucci

Theoretical and Mathematical Physics•Jul 1, 2011•23 citations

The Scalar Field Extension of Bohmian Mechanics: An Effective Field Theory with Laboratory-Testable Predictions

Kevin Bleep

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.

•Mar 9, 2026•0 citations

The Quantization of Relativistic Classical Mechanics

Herbert C. Corben

Physics Essays•Sep 1, 1995•1 citation

On quantization, the generalised Schroedinger equation and classical mechanics

K. R. W. Jones

•Jun 1, 1991•0 citations
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.