Covariant Field Dynamics in the C6 Phase Geometry: Maxwell, Dirac-like, and Geodesic Structures

Abstract We develop a fully covariant formulation of field dynamics in the six-dimensional phase geometry C6, consisting of the four-dimensional spacetime sector and a two-dimensional internal phase manifold. We present: (1) the C6–Maxwell equations with mixed and pure phase-sector field strengths; (2) a Dirac-like equation constructed from the C6 Clifford algebra; and (3) the covariant geodesic motion of classical particles in the extended geometry. All equations are shown to be invariant under the C6–Lorentz group, providing a unified geometric structure for visible and hidden phase dynamics.