Quantum Field Theory as Projection Geometry

This paper presents a reformulation of quantum field theory derived from a deeper geometric substrate termed Golden Theory—a projection-based framework governed by golden-ratio-selected coherence. In this model, quantum fields are not fundamental entities but emergent curvature modes: stable interference structures generated by coherence-preserving projection from a timeless, conformally invariant boundary. Key features of quantum field theory—including field quantization, gauge symmetry, the discrete mass spectrum, and the Yang–Mills mass gap—emerge naturally from golden-ratio scaling, projection depth, and curvature resonance thresholds. These structures arise from first principles, without free parameters or ad hoc constructions. This framework eliminates the need for conventional renormalization by introducing a geometric lower bound on field excitation energy. It also unifies vacuum fluctuations and dark matter as gravitational effects of ghost curvature: coherence-orthogonal curvature modes that remain unprojectable yet influence the emergent geometry. This work extends and applies the projection-based framework developed in: The Mathematical Principles of Natural Philosophy: On the Origin of Spacetime (D. Toupin, 2025, Zenodo:10.5281/zenodo.15626854). It also supports the proof of the Yang–Mills mass gap via projection thresholds: Proof of the Yang–Mills Mass Gap via Projection-Induced Curvature Thresholds (D. Toupin, 2025, Zenodo:10.5281/zenodo.15620214).