{
  "abstract": "We show that the concept of particles and antiparticles is related to the Weyl-Heisenberg group $W\\!H_3$. Its generators are the position operators $\\hat x^a$, the momentum operators $\\hat p_a$, and the central element $Q_{\\sf{v}}$, which defines a subgroup U(1)$_{\\sf v}$ of $W\\!H_3$. We show that the wave functions have a charge relative to the group U(1)$_{\\sf{v}}$ equal to either $q_+=1/\\hbar$ (particle $ψ_+$) or $q_-=-1/\\hbar$ (antiparticle $ψ_-$). We call these eigenvalues of the operator $Q_{\\sf{v}}$ quantum charges: $Q_{\\sf{v}}ψ_\\pm^{}=q_\\pm^{}ψ_\\pm^{}$. The wave functions $ψ_+$ and $ψ_-$ belong to the Hilbert spaces $\\mathcal{H}_+$ and $\\mathcal{H}_-$, on which unitarily inequivalent representations $π_\\hbar$ and $π_{-\\hbar}$ of the Weyl-Heisenberg group $W\\!H_3$ are defined. These representations are related to each other by the antilinear charge conjugation operator $\\hat C$, which maps $\\mathcal{H}_+, q_+$ to $\\mathcal{H}_-, q_-$. Charges $q_\\pm^{}$ are intrinsic characteristics of the wave functions $ψ_\\pm^{}$, similar to spin and electric charge. The wave function possesses one of these charges, $q_+$ or $q_-$, prior to the specification of any equations. We show that negative probabilities/energies and the Klein paradox in Klein-Gordon and Dirac theories are consequences of the violation of U(1)$_{\\sf v}$-invariance in these theories. Restoring this invariance separates particle and antiparticles and eliminates all paradoxes at the level of first-quantized relativistic theories.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29791",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander D. Popov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6mn9gf0nztqdj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29791",
  "fulltext_url": null,
  "id": "6mn9gf0nztqdj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29791",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7223207176",
  "pdf_url": "https://arxiv.org/pdf/2610.29791",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6mn9gf0nztqdj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.29791",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29791"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Charge as a Particle/Antiparticle Label",
  "title_text": "Quantum Charge as a Particle/Antiparticle Label",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/6mn9gf0nztqdj",
  "venue": "arXiv",
  "versions": []
}