{
  "abstract": "We describe the Poisson bracket of a Lagrangian field theory expressed in the framework of $L_\\infty$ algebras. If the symplectic structure on phase space is defined following recent work, we show that the Poisson bracket can be computed with the Peierls formula, confirming the well-known result of the covariant phase space formalism. Of particular interest is the Poisson bracket in nonlocal theories. In $p$-adic string theory we find that a straightforward construction of the Poisson bracket is obstructed by higher derivative instabilities. We also discuss the inverse relation between the Poisson bracket and symplectic structure in the language of homological algebra, extending some ideas in the mathematical physics literature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: JHEP11(2026)049",
  "arxiv": "2606.30630",
  "author_total": 4,
  "authors": [
    {
      "name": "Vinícius Bernardes"
    },
    {
      "name": "Theodore Erler"
    },
    {
      "name": "Atakan Hilmi Fırat"
    },
    {
      "name": "Igor Khavkine"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dj4pe30770stn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.30630",
  "fulltext_url": null,
  "id": "dj4pe30770stn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.30630",
  "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",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.30630",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dj4pe30770stn.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:04Z",
      "native_id": "2606.30630",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.30630"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Poisson bracket and $L_\\infty$ algebras",
  "title_text": "Poisson bracket and L_∞ algebras",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:07Z",
  "url": "https://research.draconitic.com/paper/dj4pe30770stn",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/jhep11(2026)049",
      "pid": "e84zr959syazr",
      "relation": "published-as",
      "title": "Poisson bracket and L∞ algebras",
      "venue": "Journal of High Energy Physics"
    }
  ]
}