{
  "abstract": "We introduce a microlocal formulation of the Schrödinger-Klein-Gordon system describing the interaction between a non-relativistic quantum particle and a Klein-Gordon field through Yukawa coupling. Instead of working directly with the Schrödinger wave function, we represent the quantum component by its Fourier-Wigner transform, and we rewrite the Klein-Gordon equation in terms of a complex Fourier variable. Eliminating the field variable yields a closed nonlinear Fourier-Moyal equation on phase space whose unknown is the Fourier-Wigner distribution associated with the quantum component. The resulting formulation provides a refined description of the particle-field interaction at the microlocal level. In particular, the original cubic coupling is transformed into a quadratic self-interaction governed by an explicit bilinear operator. This new representation permits the use of techniques from time-frequency analysis. Building on this, we develop a well-posedness theory for the Fourier-Moyal equation in anisotropic spaces involving Wiener-type norms and prescribed moduli of continuity. Local existence and uniqueness are established under general assumptions on the ultraviolet cutoff, together with propagation of microlocal regularity. We then introduce a new construction of weak L 2 -solutions by exploiting compactness properties of Fourier-Wigner transforms and obtain global existence for prepared data. The aim is to provide an alternative analytical framework for the study of Yukawa-type interactions and to establish a bridge between nonlinear dispersive equations and phase-space methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11658",
  "author_total": 2,
  "authors": [
    {
      "name": "Christophe Cheverry"
    },
    {
      "name": "Zied Ammari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fkjgqzz762em7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11658",
  "fulltext_url": null,
  "id": "fkjgqzz762em7",
  "issns": [],
  "landing_url": "https://hal.science/hal-05735305v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ap"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7212311299",
  "pdf_url": "https://hal.science/hal-05735305/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fkjgqzz762em7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:24Z",
      "native_id": "hal-05735305",
      "source": "hal",
      "url": "https://hal.science/hal-05735305v1"
    },
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11658",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11658"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "THE SCHRÖDINGER-KLEIN-GORDON SYSTEM REVISITED",
  "title_text": "THE SCHRÖDINGER-KLEIN-GORDON SYSTEM REVISITED",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/fkjgqzz762em7",
  "venue": "HAL",
  "versions": []
}