{
  "id": "oai:papers.qnfo.org:the-zitterbewegung-current-correlator-as-a-mathbb-z-2-invariant-vanishing-zbw-si",
  "slug": "the-zitterbewegung-current-correlator-as-a-mathbb-z-2-invariant-vanishing-zbw-si",
  "title": "The Zitterbewegung Current Correlator as a ℤ₂ Invariant: Vanishing ZBW Signal as a Hardware-Level Diagnostic of the Majorana Condition",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Certifying that a candidate excitation in a topological-qubit device is a true Majorana zero mode rather than an ordinary Dirac fermion or a trivial Andreev bound state remains an unsolved hardware-level problem, and the same Dirac-versus-Majorana question has consumed decades of effort in neutrino physics. Existing discriminators rely on indirect signatures — tunnelling spectroscopy, interferometric braiding, neutrinoless double-beta decay — that require long coherence times, active error correction, or tonne-scale detectors. We analyze the Zitterbewegung (ZBW) contribution to the current–current correlator ⟨ j^μ(x)j^ν(0)⟩ in (2+1) dimensions and derive, from the collapse of the independent particle–antiparticle operator algebra under the self-conjugacy constraint ψ=ψ^c, that the ZBW term vanishes identically for a Majorana field while remaining finite for a Dirac field. The resulting order parameter O_ZBW, the ratio of the ZBW to the static correlator contribution, therefore takes only the values $0$ (Majorana) and a non-zero Dirac value growing with momentum to ≈ 0.92, defining a Z₂ invariant. We verify the Dirac-case ratios $1.0000$, $0.8944$, $0.6863$, $0.2981$ at p=0, $0.5$, $1$, $2$ by independent arithmetic, confirm the Compton-scale inputs ω_C ≈ 1.55× 10²1 Hz and λ_C/2 ≈ 1.93× 10^-13 m from first constants, and show that the reported 57\\% edge reduction of the ZBW transition graph exceeds the 50\\% bound implied by state pairing alone. The invariant defines a projective, perturbation-stable readout target that would let a qubit-lab engineer accept or reject a device with a single binary measurement.",
  "abstract_markdown": "Certifying that a candidate excitation in a topological-qubit device is a true Majorana zero mode rather than an ordinary Dirac fermion or a trivial Andreev bound state remains an unsolved hardware-level problem, and the same Dirac-versus-Majorana question has consumed decades of effort in neutrino physics. Existing discriminators rely on indirect signatures — tunnelling spectroscopy, interferometric braiding, neutrinoless double-beta decay — that require long coherence times, active error correction, or tonne-scale detectors. We analyze the Zitterbewegung (ZBW) contribution to the current–current correlator $\\langle j^\\mu(x)j^\\nu(0)\\rangle$ in $(2+1)$ dimensions and derive, from the collapse of the independent particle–antiparticle operator algebra under the self-conjugacy constraint $\\psi=\\psi^{c}$, that the ZBW term vanishes identically for a Majorana field while remaining finite for a Dirac field. The resulting order parameter $\\mathcal{O}_{\\text{ZBW}}$, the ratio of the ZBW to the static correlator contribution, therefore takes only the values $0$ (Majorana) and a non-zero Dirac value growing with momentum to $\\approx 0.92$, defining a $\\mathbb{Z}_2$ invariant. We verify the Dirac-case ratios $1.0000$, $0.8944$, $0.6863$, $0.2981$ at $p=0$, $0.5$, $1$, $2$ by independent arithmetic, confirm the Compton-scale inputs $\\omega_C \\approx 1.55\\times 10^{21}$ Hz and $\\lambda_C/2 \\approx 1.93\\times 10^{-13}$ m from first constants, and show that the reported $57\\%$ edge reduction of the ZBW transition graph exceeds the $50\\%$ bound implied by state pairing alone. The invariant defines a projective, perturbation-stable readout target that would let a qubit-lab engineer accept or reject a device with a single binary measurement.",
  "date": "2026-11-03",
  "first_published": "2026-11-03",
  "last_revised": "2026-11-03T00:00:00Z",
  "modified": "2026-11-03T00:00:00Z",
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  "peer_review_status": "Not independently peer-reviewed",
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  "doi": null,
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  "url": "https://papers.qnfo.org/papers/the-zitterbewegung-current-correlator-as-a-mathbb-z-2-invariant-vanishing-zbw-si",
  "license_url": "https://legal.qnfo.org/",
  "license_spdx": null,
  "sha256": "202607aa89013fe420fbb60a8a31adb056490dd7610ee0504c4583c8489cabf1",
  "version_url": "https://papers.qnfo.org/papers/the-zitterbewegung-current-correlator-as-a-mathbb-z-2-invariant-vanishing-zbw-si/v/1.0.0",
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    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "The Zitterbewegung Current Correlator as a ℤ₂ Invariant: Vanishing ZBW Signal as a Hardware-Level Diagnostic of the Majorana Condition"
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    ],
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    "publicationYear": "2026",
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        "description": "Certifying that a candidate excitation in a topological-qubit device is a true Majorana zero mode rather than an ordinary Dirac fermion or a trivial Andreev bound state remains an unsolved hardware-level problem, and the same Dirac-versus-Majorana question has consumed decades of effort in neutrino physics. Existing discriminators rely on indirect signatures — tunnelling spectroscopy, interferometric braiding, neutrinoless double-beta decay — that require long coherence times, active error correction, or tonne-scale detectors. We analyze the Zitterbewegung (ZBW) contribution to the current–current correlator ⟨ j^μ(x)j^ν(0)⟩ in (2+1) dimensions and derive, from the collapse of the independent particle–antiparticle operator algebra under the self-conjugacy constraint ψ=ψ^c, that the ZBW term vanishes identically for a Majorana field while remaining finite for a Dirac field. The resulting order parameter O_ZBW, the ratio of the ZBW to the static correlator contribution, therefore takes only the values $0$ (Majorana) and a non-zero Dirac value growing with momentum to ≈ 0.92, defining a Z₂ invariant. We verify the Dirac-case ratios $1.0000$, $0.8944$, $0.6863$, $0.2981$ at p=0, $0.5$, $1$, $2$ by independent arithmetic, confirm the Compton-scale inputs ω_C ≈ 1.55× 10²1 Hz and λ_C/2 ≈ 1.93× 10^-13 m from first constants, and show that the reported 57\\% edge reduction of the ZBW transition graph exceeds the 50\\% bound implied by state pairing alone. The invariant defines a projective, perturbation-stable readout target that would let a qubit-lab engineer accept or reject a device with a single binary measurement.",
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