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  "id": "oai:papers.qnfo.org:from-operational-axioms-to-field-axioms-an-audit-of-the-gpt-to-wightman-reconstr",
  "slug": "from-operational-axioms-to-field-axioms-an-audit-of-the-gpt-to-wightman-reconstr",
  "title": "From Operational Axioms to Field Axioms: An Audit of the GPT-to-Wightman Reconstruction Claim for Systems with Infinitely Many Degrees of Freedom",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Operational reconstructions of quantum theory have clarified the status of finite-dimensional quantum mechanics, but no published derivation takes the operational axioms of generalized probabilistic theories (GPTs) as hypotheses and produces the Wightman axioms of relativistic quantum field theory as conclusions. This gap leaves physicists unable to say which parts of quantum field theory structure are forced by operational quantum probability and which are independent relativistic input. We formalize four GPT axioms—causality, no-signaling, local tomography, and continuous reversibility—in the operator-algebraic setting of nets of von Neumann algebras, and audit each step of the claimed reconstruction against the Wightman and algebraic field theory literature. We prove that causality and no-signaling imply microcausality for localized observables; we exhibit fermionic theories, whose local state spaces violate local tomography while satisfying the graded Wightman axioms, as counterexamples showing local tomography cannot be necessary; we show continuous reversibility yields a strongly continuous unitary Poincaré representation but not the spectrum condition, which must be added as a fifth axiom; and we show real and quaternionic Hilbert-space theories satisfy all four operational axioms, so the reconstruction selects a family of theories rather than complex QFT uniquely. Of the five structural pillars audited, 1 is derived, 2 are conditional, and 2 are underived. The claim is therefore a conjecture with one proven pillar, two conditional pillars, and two unproven pillars, and we state the lemmas whose proof or refutation would settle it.",
  "abstract_markdown": "Operational reconstructions of quantum theory have clarified the status of finite-dimensional quantum mechanics, but no published derivation takes the operational axioms of generalized probabilistic theories (GPTs) as hypotheses and produces the Wightman axioms of relativistic quantum field theory as conclusions. This gap leaves physicists unable to say which parts of quantum field theory structure are forced by operational quantum probability and which are independent relativistic input. We formalize four GPT axioms—causality, no-signaling, local tomography, and continuous reversibility—in the operator-algebraic setting of nets of von Neumann algebras, and audit each step of the claimed reconstruction against the Wightman and algebraic field theory literature. We prove that causality and no-signaling imply microcausality for localized observables; we exhibit fermionic theories, whose local state spaces violate local tomography while satisfying the graded Wightman axioms, as counterexamples showing local tomography cannot be necessary; we show continuous reversibility yields a strongly continuous unitary Poincaré representation but not the spectrum condition, which must be added as a fifth axiom; and we show real and quaternionic Hilbert-space theories satisfy all four operational axioms, so the reconstruction selects a family of theories rather than complex QFT uniquely. Of the five structural pillars audited, 1 is derived, 2 are conditional, and 2 are underived. The claim is therefore a conjecture with one proven pillar, two conditional pillars, and two unproven pillars, and we state the lemmas whose proof or refutation would settle it.",
  "date": "2026-11-02",
  "first_published": "2026-11-02",
  "last_revised": "2026-11-02T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/from-operational-axioms-to-field-axioms-an-audit-of-the-gpt-to-wightman-reconstr",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "From Operational Axioms to Field Axioms: An Audit of the GPT-to-Wightman Reconstruction Claim for Systems with Infinitely Many Degrees of Freedom"
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