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  "slug": "adelic-zitterbewung-p-adic-regularization-of-dirac-trembling-motion-and-the-prod",
  "title": "Adelic Zitterbewegung: p-Adic Regularization of Dirac Trembling Motion and the Product-Formula Cancellation at Macroscopic Scales",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Zitterbewegung (ZBW) — the trembling motion of Dirac wave packets at the Compton scale — is conventionally treated as a purely Archimedean interference effect between the positive- and negative-energy branches of the free Dirac equation. Missing from the standard account is any mechanism by which the non-Archimedean completions of the rationals could enter the dynamics, and any quantitative statement of when such contributions would or would not matter. We propose a conjectural framework in which the free Dirac equation is formulated over the adele ring A = R × ∏_p Q_p, so that the trembling motion acquires simultaneous oscillatory components in the real sector and in every p-adic sector, and we define a sector-resolved velocity expectation together with a cancellation mechanism in which the p-adic contributions to macroscopic motion are suppressed by the adele product formula |x|_∞ ∏_p |x|_p = 1. [...]",
  "abstract_markdown": "Zitterbewegung (ZBW) — the trembling motion of Dirac wave packets at the Compton scale — is conventionally treated as a purely Archimedean interference effect between the positive- and negative-energy branches of the free Dirac equation. Missing from the standard account is any mechanism by which the non-Archimedean completions of the rationals could enter the dynamics, and any quantitative statement of when such contributions would or would not matter. We propose a conjectural framework in which the free Dirac equation is formulated over the adele ring $\\mathbb{A} = \\mathbb{R} \\times \\prod_p \\mathbb{Q}_p$, so that the trembling motion acquires simultaneous oscillatory components in the real sector and in every $p$-adic sector, and we define a sector-resolved velocity expectation together with a cancellation mechanism in which the $p$-adic contributions to macroscopic motion are suppressed by the adele product formula $|x|_\\infty \\prod_p |x|_p = 1$. [...]",
  "date": "2026-10-11",
  "first_published": "2026-10-11",
  "last_revised": "2026-10-14T07:16:05Z",
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  "url": "https://papers.qnfo.org/papers/adelic-zitterbewung-p-adic-regularization-of-dirac-trembling-motion-and-the-prod",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Adelic Zitterbewegung: p-Adic Regularization of Dirac Trembling Motion and the Product-Formula Cancellation at Macroscopic Scales"
      }
    ],
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    "dates": [
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        "date": "2026-10-11",
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        "description": "Zitterbewegung (ZBW) — the trembling motion of Dirac wave packets at the Compton scale — is conventionally treated as a purely Archimedean interference effect between the positive- and negative-energy branches of the free Dirac equation. Missing from the standard account is any mechanism by which the non-Archimedean completions of the rationals could enter the dynamics, and any quantitative statement of when such contributions would or would not matter. We propose a conjectural framework in which the free Dirac equation is formulated over the adele ring A = R × ∏_p Q_p, so that the trembling motion acquires simultaneous oscillatory components in the real sector and in every p-adic sector, and we define a sector-resolved velocity expectation together with a cancellation mechanism in which the p-adic contributions to macroscopic motion are suppressed by the adele product formula |x|_∞ ∏_p |x|_p = 1. [...]",
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