Complementary Phase Geometry: Massless Particle Dynamics, Helicity Sectors, and Null Maxwell Solutions
The massless sector of Complementary Phase Geometry (CPG) is formulated using real $Cl(3,4)$ generating geometry and a distinct selected kinetic quadratic form. Its central Clifford-geometric result is the decomposition of a transverse polarization module by the relative-orientation involution between ordinary and complementary rotation planes. Within the two resulting circular eigensectors, complementary phase rotations are exactly equivalent to ordinary axial rotor transformations of opposite unit weights. The selected massless kinetic constraint admits the conventional reparametrization-invariant canonical parent and an invariant ordinary-luminal branch. Its Hamilton--Jacobi material phase is constant along each free null characteristic. Phase equivariance determines the phase dependence of transverse observable maps, while real linearity and axial covariance classify their reference maps. Ordinary transverse reflection covariance fixes the reference map up to amplitude and phase origin; their conventional choice selects the ordinary-component projection. The resulting ordinary null-bivector profiles satisfy a restricted family of source-free Maxwell equations. The physical observable correspondence, intrinsic helicity normalization, and relation to the massive CPG rotor remain open.
Authors
- Evren Belenlioğlu
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-10-29
- DOI
- https://doi.org/10.5281/zenodo.23761756
- Primary Topic
- Algebraic and Geometric Analysis
- Type
- preprint