{
  "abstract": "We establish a rigorous functional-analytic framework for the imaginary component $p_I$ of the complex weak momentum $p_Q = p_R + ip_I = \\frac{\\hbar}{i}\\nabla\\lnψ$. For every wavefunction in the Sobolev space $H^1(Ω)$, including those with nodal sets, we prove that the expectation value of $p_I$ vanishes identically, as a consequence of the regularity of $ρ= |ψ|^2$ and without appeal to the polar form $ψ= Re^{iS/\\hbar}$. We further show that \\textnormal{(i)} the Bohm quantum potential arises entirely from $p_I$ and satisfies $\\langle V_{\\mathrm{qu}}\\rangle = \\langle p_I^2\\rangle/2m$, from which the known Fisher information relation follows as a corollary; \\textnormal{(ii)} the group velocity of a Bloch band is the density-weighted average of $p_R/m$, with no contribution from $p_I$; \\textnormal{(iii)} the decomposition is gauge-invariant under magnetic minimal coupling, the vector potential acting only on $p_R$; and \\textnormal{(iv)} the results extend to curved Riemannian manifolds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12112",
  "author_total": 1,
  "authors": [
    {
      "name": "A. N. Khondker"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f7g4qd4a1wnqj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12112",
  "fulltext_url": null,
  "id": "f7g4qd4a1wnqj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12112",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.12112",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f7g4qd4a1wnqj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.12112",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12112"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The Imaginary Component of the Weak Momentum: Spectral Vanishing and Gauge Invariance",
  "title_text": "The Imaginary Component of the Weak Momentum: Spectral Vanishing and Gauge Invariance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/f7g4qd4a1wnqj",
  "venue": "arXiv",
  "versions": []
}