P-QFT: The Geometric Reduction of Quantum Field Theory — From Spatial Micro-elements to Feynman Rules

Abstract:Quantum field theory (QFT) is the most successful framework for describing microscopic particles and their interactions, yet its foundations — field quantisation, gauge symmetry, Feynman rules — are treated as primitive postulates. Based on Space Ontology, we systematically demonstrate that all core structures of QFT emerge from a logically prior, Planck-scale, classical geometric model. We posit that space at the Planck scale is composed of interacting "vortex micro-elements", whose dynamics are governed solely by two fundamental instincts — alignment (J) and twisting (K) — characterised by the single dimensionless free parameter κ = K/(J l_Pl) ≈ 0.017. Starting from this model, we rigorously show: (1) the continuum limit of the partition function is exactly the path integral of QFT; (2) fermion fields emerge as collective coordinates of vortex solitons, with their three-generation structure corresponding to representations of the 2T × C₃ group; (3) the Higgs mechanism is reduced to a condensation phase transition of space itself, with the hierarchy problem resolved by a geometric dilution factor G(κ) ≈ 4.2×10³¹; (4) Abelian and non-Abelian gauge fields and their interaction vertices arise from geometric couplings and chiral correlations of spatial fluctuations, with the SU(3) structure constants emerging from the differential geometry of the colour-space 7-sphere; and (5) the "mysterious" phenomena of quantum mechanics — wave-particle duality, Bell inequality violation, tunnelling, and measurement collapse — are all reduced to manifestations of classical geometric entanglement entropy under different conditions. We conclude that QFT is not an ultimate description of nature, but an effective theory of a deeper, deterministic classical geometric dynamics. This paper is the capstone of the first series (17 papers total) of Space Ontology, providing a complete closure of the argument for this new paradigm of physics.