Abstract

This paper completes the quantum formalism of the Axis Model, a geometric unification framework in which all observable particles are constructed as scalar-stabilized tri-vector composites known as mortons. We derive the full operator content of the scalar, vector, and fermionic sectors; construct the gauge–covariant derivative from internal projection geometry; dynamically derive the electroweak SU(2)L × U(1)Y  sector; and demonstrate BRST invariance, unitarity, and anomaly cancellation. The gauge fields arise as projections of Abelian vector modes onto internal symmetry generators, and scalar coherence enforces both gauge invariance and topological consistency. We show that the quantum theory is renormalizable and radiatively stable throughout the effective-field-theory window EIR < µ < min(ΛΦ, Λq), with a scalar-coherence cutoff ΛΦ ∼ 105 GeV and a morton-dissolution scale Λq ∼ 1016 GeV. Within this window, all low-energy predictions match the Standard Model, and in the infrared the theory reduces to a constrained SMEFT with sub-percent operator deviations. Taken together, these results establish the Axis Model as a quantum-consistent effective field theory across its validity window.

Keywords: Unified Field Theory, Scalar field, anomaly cancellation, BRST quantization, effective field theory, Standard Model, renormalization group, gauge symmetry, quantum field theory, internal geometry, electroweak unification.