The Emergence of Relativistic Quantum Field Theory from the Admissibility Conditions for Coherent Projection

The Quantum Blueprint Formalism (QBF) has derived nonrelativistic quantum mechanics — the Schrödinger equation — as the circulation-dominated limit of the Mother Equation on the pre-coherent possibility space M_s (Schmieke, 2026r). That derivation operates in a finite-dimensional phase space and therefore yields quantum mechanics for a fixed number of particles. However, the Standard Model is a relativistic quantum field theory (QFT), requiring: (i) infinitely many degrees of freedom, (ii) creation and annihilation of particles, (iii) Lorentz invariance, (iv) the spin-statistics theorem, and (v) ultraviolet regulation. This paper extends the derivation to the full infinite-dimensional structure of M_s and shows how these five features arise from the same admissibility conditions (A1)–(A3) and the same Mother Equation, given the additional assumption that M_s is an infinite-dimensional separable Hilbert manifold (Assumption 2.1). Second quantization, the Klein–Gordon equation, Fock space, and Lorentz invariance are derived. The Dirac equation is constrained (it follows if the circulation field carries spinor structure). The spin-statistics connection is derived for free fields and constrained for interacting fields (requiring perturbative microcausality). A natural ultraviolet cutoff follows qualitatively from (A3); the specific scaling is motivated but not yet rigorously proven.