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