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LRT Constraints on QFT: Deriving Fock Structure and Interpreting Renormalization from Logical Foundations

James (JD) Longmire

Published Dec 1, 2025• 0 citations
Publisher

Abstract

Logic Realism Theory (LRT) derives non-relativistic quantum mechanics from the claim that the Three Fundamental Laws of Logic are ontological constraints constitutive of physical distinguishability. This paper extends LRT to quantum field theory through a tiered derivation structure with explicit physical inputs at each level. We establish three principal results: (1) Fock space structure is derived from LRT axioms plus Lorentz invariance and locality; (2) the spin-statistics connection follows from Lorentz invariance and microcausality via the standard Pauli argument; (3) the uniqueness of complex QFT is established. The paper distinguishes derivations from interpretations. Cluster decomposition, vacuum uniqueness, and the spectral gap are physical inputs (Tier 4), not consequences of logical constraints. Renormalization is interpreted as 3FLL-restoration at UV scales, but this does not derive renormalization group equations. Four predictions and six strong falsifiers are identified.

DOI
10.5281/zenodo.17779065

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Logic Realism Theory (LRT) derives non-relativistic quantum mechanics from the claim that the Three Fundamental Laws of Logic are ontological constraints constitutive of physical distinguishability. This paper extends LRT to quantum field theory through a tiered derivation structure with explicit physical inputs at each level. We establish three principal results: (1) Fock space structure is derived from LRT axioms plus Lorentz invariance and locality; (2) the spin-statistics connection follows from Lorentz invariance and microcausality via the standard Pauli argument; (3) the uniqueness of complex QFT is established. The paper distinguishes derivations from interpretations. Cluster decomposition, vacuum uniqueness, and the spectral gap are physical inputs (Tier 4), not consequences of logical constraints. Renormalization is interpreted as 3FLL-restoration at UV scales, but this does not derive renormalization group equations. Four predictions and six strong falsifiers are identified.
Logic Realism Theory (LRT) proposes that the Three Fundamental Laws of Logic (3FLL)—Identity, Non-Contradiction, and Excluded Middle—are not merely rules of reasoning but ontological constraints constitutive of physical distinguishability. The core evidence is an asymmetry: we can conceive of 3FLL violations, yet physical reality never produces them. This asymmetry indicates that 3FLL constrain reality, not merely cognition. This paper develops the philosophical foundations of this claim. We argue that: (1) 3FLL have a dual character, functioning both epistemically and ontologically; (2) quantum mechanics emerges as the unique "interface" structure mediating between non-Boolean possibility and Boolean actuality; (3) this framework resolves longstanding interpretive puzzles while maintaining scientific realism. The result is a form of structural realism grounded in logical necessity rather than contingent physical law.
This companion paper provides the rigorous mathematical constructions underlying Logic Realism Theory. We prove three key results: (1) the Hardy kernel construction derives inner product structure directly from the distinguishability metric D without presupposing Hilbert space or the Born rule; (2) LRT axioms imply all five Masanes-Müller axioms, including MM5 (entanglement connectivity) via the Lee-Selby theorem applied to CBP-enforced purification uniqueness; (3) complex quantum mechanics is the unique theory satisfying LRT axioms. The derivation chain from logical constraints (3FLL) to quantum mechanics is complete—no conditional hedges or irreducible gaps remain.
Every physical measurement ever conducted has yielded exactly one outcome: self-identical, non-contradictory, determinate. This paper argues that the Three Fundamental Laws of Logic (Identity, Non-Contradiction, and Excluded Middle) are not cognitive conventions but ontological constraints constitutive of physical distinguishability. From this thesis, quantum mechanics emerges as the unique stable structure at the interface between non-Boolean possibility and Boolean actuality. The framework derives rather than postulates: complex Hilbert space structure follows from interface constraints combined with the physical requirement of compositional consistency (local tomography); the Born rule follows from Gleason's theorem; unitary dynamics follows from information preservation requirements. One structural prediction, that quantum mechanics requires complex amplitudes, has been experimentally confirmed (Renou et al., 2021). The framework specifies twelve explicit conditions that would falsify it. Logic Realism Theory provides unified explanation for seventeen quantum phenomena that other interpretations treat as independent postulates, while maintaining realism, locality, and parsimony.
This working paper derives quantum non-decomposability, Bell's theorem, and Kochen-Specker contextuality from Logic Realism Theory's single foundational equation A_Ω = L₃(I∞), where I∞ is the Infinite Information Space, L₃ is the Three Fundamental Laws of Logic acting as a selection functional, and A_Ω is the actualized domain. The paper establishes that LRT is a one-equation theory: all results are downstream of the core equation with no independent primitives introduced. Key results: (1) the Unique Necessary Successor (UNS) constraint is derived as a theorem of L₃ via Identity and Excluded Middle, tightened by Leibniz Identity of Indiscernibles; (2) quantum probability is reinterpreted as epistemic underdetermination of state description, with the Born rule as the unique consistent measure over incomplete descriptions via Gleason; (3) the Joint Resolution Condition (JRC) is proved equivalent to Schmidt rank > 1, establishing that entangled states are logically forced by tensor product structure; (4) the Non-Decomposability Theorem shows that decomposing a JRC-satisfying configuration into local sub-descriptions necessarily violates Excluded Middle; (5) Bell's theorem and Kochen-Specker contextuality follow as downstream consequences. LRT is distinguished from hidden variable programs (Bohm, 't Hooft) by its grounding direction: from logic to physics, not from physics to supplemented physics. Three open formalizations for Lean 4 are identified.
We present a derivation of the Born rule from the ontological constraints imposed by the Three Fundamental Laws of Logic (L₃) within the Logic Realism Theory (LRT) framework. The central argument proceeds through five stages: (1) L₃ constraints at the vehicle level require that physical systems possess determinate dispositions toward measurement outcomes; (2) these dispositions must satisfy vehicle‑weight invariance—probability assignments cannot depend on the descriptive decomposition chosen; (3) vehicle‑weight invariance, combined with finite additivity, yields the premises of Gleason‑type theorems; (4) Gleason’s theorem then forces the trace form μ(P) = Tr(ρP) for all projectors; (5) for pure states, this reduces to the Born rule p = |⟨φ|ψ⟩|².[Attachment] We provide both an intuitive derivation chain and a formal axiom presentation (A1–A7) suitable for rigorous development. The derivation is non‑circular: L₃ constraints are conceptually and logically prior to the probability measure they entail. We situate this result within the quantum reconstruction literature and discuss implications for foundational physics.
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.