Abstract:   A mathematical framework is introduced in which gauge symmetries and field interactions are unified through a higher-dimensional geometric structure. The special orthogonal gauge group R(3)SO(3), embedded in $\mathbb R^9$, supports a formulation where Maxwell’s equations, spatial quantisation, and interaction fields arise naturally from a shared underlying principle.

At the core lies a system of field equations involving vector cross and dot operations that reproduce classical Maxwell behaviour while suggesting deeper topological and structural constraints. These field equations further imply a discrete geometry of space, potentially addressing questions of quantisation and field stability from first principles.

This approach offers a mathematically smooth, singularity-free alternative to conventional Lie-algebra-based gauge theories, embedding known field laws in a structure that supports both unification and quantisation. In this setting, gravitational and weak interactions may be seen as emergent from symmetry breaking, while solitonic structures offer insight into particle structure, mass, and charge.

The framework proposes a generalisation of gauge theory that invites further examination—both as a conceptual unification and as a constructive model for fundamental physical interactions.

Key Words:   Maxwell Equations, Topological solitons, Quantised Space, Quantised Charge, Gravity, Cyclic Universe

Posted in:   3 Causal Approach to Quantum Phenomena

Article Reference:   1965

Article Status: Preprint

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