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

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
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preprint

Complementary Phase Geometry: Massless Particle Dynamics, Helicity Sectors, and Null Maxwell Solutions

Evren Belenlioğlu
2 links
Zenodo (CERN European Organization for Nuclear Research)
Algebraic and Geometric Analysis
preprint

Complementary Phase Geometry: Massless Particle Dynamics, Helicity Sectors, and Null Maxwell Solutions

Evren Belenlioğlu
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Algebraic and Geometric Analysis
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Complementary Phase Geometry: Massless Particle Dynamics, Helicity Sectors, and Null Maxwell Solutions — Evren Belenlioğlu · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS