{
  "abstract": "Standard weak-lensing calculations treat lensing as a linear remapping of the matter field along the line of sight. We instead formulate lensing as a stochastic field theory for the Sachs optical scalars, driven by random Ricci-focusing and Weyl-shearing fields. With convergence and shear expressed linearly in the Sachs-scalar fluctuations, the resulting path integral generates a diagrammatic expansion for their $n$-point correlation functions, organised into linear response, nonlinear propagation, and driving-field cumulants. The conventional calculation emerges as the lowest-order, linear-propagation limit. Beyond it, nonlinear Sachs evolution couples to driving-field non-Gaussianity, mixing the matter cumulant hierarchy into the lensing hierarchy. A selection rule governs the couplings: an $n$-point observable receives a direct contribution from the $n$-point driving-field cumulant, and its leading hierarchy-mixing correction from the $(n+1)$-point cumulant via one nonlinear Sachs interaction, with higher cumulants entering only at higher order. The two-point function, for instance, receives corrections from three-point cumulants of Ricci focusing and Weyl shearing through nonlinear Sachs evolution. Rather than a restrictive approximation scheme, the formalism is a paradigm shift: a unified framework naturally accommodating path corrections, higher-order matter statistics, stochasticity, and small-scale effects.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.19472",
  "author_total": 4,
  "authors": [
    {
      "name": "Zheng Zhang"
    },
    {
      "name": "Philip Bull"
    },
    {
      "name": "Chris Clarkson"
    },
    {
      "name": "Andrina Nicola"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/74pv756fj6yw7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.19472",
  "fulltext_url": null,
  "id": "74pv756fj6yw7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.19472",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.CO"
    ],
    [
      "arxiv",
      "gr-qc"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.19472",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/74pv756fj6yw7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2606.19472",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.19472"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Statistical Field Theory for Weak Gravitational Lensing",
  "title_text": "Statistical Field Theory for Weak Gravitational Lensing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:36Z",
  "url": "https://research.draconitic.com/paper/74pv756fj6yw7",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/w3tj-slzm",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}