Geometric Unification of Quantum Mechanics and Nuclear Forces within Zhang Xiangqian's Unified Field Theory Framework

This paper systematically completes the first-principles geometric reconstruction from non-relativistic quantum mechanics, relativistic quantum mechanics, to quantum electrodynamics and the Yukawa potential of nuclear forces under the core paradigm of "physics is geometry" in Zhang Xiangqian's Unified Field Theory (UFT).All derivations logically originate from three core postulates—the cylindrical helical motion of light in spacetime, the light-speed constraint equation, and the geometrization postulate—thoroughly reducing fundamental physical quantities such as mass, charge, energy, and momentum to metrics of spacetime geometric properties.

 Key achievements include:

1.  Geometrization of quantum mechanics: Strictly deriving both time-dependent and stationary Schrödinger equations from the mass-frequency equivalence principle and the periodicity of cylindrical helical motion, independently via two distinct pathways;Revealing that the square of the wave function modulus represents the number density of spacetime vibration units, with position and momentum operators, commutation relations, and the uncertainty principle all stemming from spacetime geometric stability constraints and Fourier duality; Utilizing the geometrically derived fine-structure constant to fully geometrize the Coulomb potential, precisely calculating hydrogen atom ground state parameters with a relative error of magnitude.

2.  Geometrization of Electromagnetic Fields and Relativistic Quantum Mechanics: Interpreting electromagnetic potentials from spacetime flexural fields, deriving the minimal coupling principle and the spacetime phase redundancy essence of gauge symmetries;Quantization of electromagnetic fields based on UFT electromagnetic constants, where photons are quantum excitations of the torsion field ( ); natural derivation of the Klein-Gordon equation and Dirac equation from UFT kinematic relations, providing clear geometric origins for spin and factors ( ), and interpreting antimatter as chirally flipped spacetime vortices.

3.  Geometrization of Quantum Electrodynamics: Mappings of QED's electromagnetic field quantization, interaction vertices, path integrals, Feynman rules, and observable effects (anomalous magnetic moments, Lamb shifts) to quantum oscillations and geometric phase accumulation in spacetime flexure fields. Coupling constants are topologically locked by spacetime, with all low-energy predictions exhibiting high experimental consistency.

4.  Geometrization of the Yukawa Potential for Nuclear Forces: Treating protons as spacetime topological solitons, utilizing the critical geometric condition at the proton boundary and microscopic geometric approximation , we derive the global inertia ratio at the proton boundary for the first time without relying on nuclear force experimental data;Strict derivation of meson mass and nuclear force range and from compactification quantization of proton boundary helical orbits (periodic boundary conditions) , with experimental self-consistent determination ;Deriving the massive Yukawa potential equation via 5-dimensional Kaluza-Klein dimensional reduction, solving for the nucleon-nucleon potential , and calculating the potential depth yields results highly consistent (0.6% error) with the phenomenological values of the high-precision nuclear force potential Argonne v18 . The coupling constant running decreases from 14.0 at the center to 0.71 at the boundary, consistent with both qualitative and quantitative low-energy nuclear force experiments.

5.  Unification of Four Forces: Within the UFT unified dynamical equation , it is rigorously demonstrated that the nuclear force term is equivalent to the negative gradient of the Yukawa potential in the static limit. This unifies electromagnetic, magnetic, gravitational, and nuclear forces into a single geometric dynamical equation, achieving a geometric unified description of the four fundamental interactions.

 All derivations undergo SI-dimensional verification, with numerical calculations based on CODATA 2018 and PDG 2022 fundamental constants. First-principles outputs are rigorously distinguished from experimentally calibrated inputs, ensuring logical consistency and reproducibility.This work signifies that the UFT paradigm of "physics is geometry" has extended from classical physics and quantum mechanics to quantum field theory and strong interactions, laying a solid foundation for ultimately achieving a unified geometric description of all interactions.

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