Curvature Electromagnetism: Deriving Maxwell from Geometry
Part III of the Curvature Field Series (A Minimal Geometric Route to Maxwell)
DOI:
https://doi.org/10.51094/jxiv.1770Keywords:
Curvature Electromagnetism, Deriving Maxwell, Constitutive laws, Uniaxial anisotropy, Berry-like connection, Aharonov–Bohm regularization, TE/TM mode ratio, Sub-percent limitAbstract
This work re-forms electromagnetism through Curvature Electromagnetism, treating the fundamental field as curvature. We set the action of the curvature field Φ\PhiΦ and the associated variational conditions so that conservation laws and the continuity equation arise in gauge-invariant form, deriving Maxwell’s equations without introducing additional non-geometric hypotheses. For both static and dynamical configurations, we gather boundary contributions, source coupling, and propagation properties into a single suite of standardized invariants, enabling a transparent equivalence check—with room to register any small deviations—against the conventional equations. The construction continues the Curvature Field series and preserves the same fixed policy and validation rules used in Part I (quantum domain) and Part II (macroscopic gravity). In this way, one curvature field organizes observables across scales, while providing a reproducible verification path (boundary-value tests, mode analysis, and source–response checks). Rather than declaring a grand unification, the paper is designed as a stepwise derivation with a practical checklist that readers can independently audit.
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