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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Phase Dynamics Framework: Variational Principle, Quantum Potential, Classical Limit, and Mapping to Hamilton–Jacobi and Madelung Formulations

Authors: صهيب زائد عوض الكريم النور, Souhaib Zayed Awad Alkarim Alnur;

Phase Dynamics Framework: Variational Principle, Quantum Potential, Classical Limit, and Mapping to Hamilton–Jacobi and Madelung Formulations

Abstract

This work presents a rigorous mathematical framework for phase dynamics in configuration space. All physical dynamics are derived from a smooth phase field Φ without assuming forces, particles, or fundamental time. The framework introduces the Euler–Phase equation, derives the unique quantum potential, and recovers classical mechanics in the limit κ → 0. It includes explicit mappings to Hamilton–Jacobi and Madelung formulations, gauge symmetry analysis, circulation quantization, and a comparison of Phase Dynamics with classical and quantum mechanics. This unified approach generalizes both CM and QM, allowing topologically nontrivial and multi-valued phase structures.

Keywords

Phase dynamics, Quantum potential, Hamilton–Jacobi, Madelung, Classical limit, Variational principle, Gauge symmetry, Circulation quantization, Schrödinger equation

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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Average
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