{
  "abstract": "We construct a class of integrable chiral fermionic quantum field theories with interactions that depend on both space and time. The construction starts from a unitary, regular, difference-form two-body scattering matrix satisfying braiding unitarity and the Yang--Baxter equation. Each freely moving right- or left-moving particle carries a characteristic coordinate that remains constant along its trajectory, and the scattering matrix depends on differences of these coordinates. The many-body amplitudes form a discrete connection over the coordinate-ordering sectors. The Yang--Baxter equation gives local path independence, while periodic winding on a spatial circle produces quantum Knizhnik--Zamolodchikov (qKZ) difference equations expressing global flatness. Once a reference amplitude satisfying the exchange and qKZ constraints is specified, these transport equations determine the exact wavefunction in every fixed-particle-number sector. Independent reparametrizations of the right- and left-moving characteristics give couplings that depend on both space and time. For the chiral $SU(2)$ Gross--Neveu realization, we solve the qKZ equations for this full characteristic family using off-shell Bethe vectors. The resulting amplitudes are written in the characteristic labels, and their pullbacks give exact many-body wavefunctions for the corresponding space-time-dependent couplings. The two-body amplitude is a ratio of Gamma functions that resums the phase shifts from successive scattering processes. Equal-slope affine maps give a spatially homogeneous specialization in which the coupling depends only on time, and the Bethe ansatz with constant coupling is recovered when the qKZ step vanishes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13377",
  "author_total": 1,
  "authors": [
    {
      "name": "Pradip Kattel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d6w7gjs2xnd58.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13377",
  "fulltext_url": null,
  "id": "d6w7gjs2xnd58",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13377",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nlin.SI"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7213358770",
  "pdf_url": "https://arxiv.org/pdf/2609.13377",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d6w7gjs2xnd58.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2609.13377",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13377"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Integrable Chiral Quantum Field Theories with Spacetime-Dependent Interactions",
  "title_text": "Integrable Chiral Quantum Field Theories with Spacetime-Dependent Interactions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/d6w7gjs2xnd58",
  "venue": "arXiv",
  "versions": []
}